Cell organization and transmission schemes in a wide area positioning system

ABSTRACT

A position location system comprises transmitters that broadcast positioning signals. Each broadcasted positioning signal comprises a pseudorandom ranging signal. The position location system includes a remote receiver that acquires and measures the time of arrival of the positioning signals received at the remote receiver. During an interval of time, at least two positioning signals are transmitted concurrently by the transmitters and received concurrently at the remote receiver. The two positioning signals have carrier frequencies offset from one another by an offset that is less than approximately twenty-five percent of the bandwidth of each positioning signal of the two positioning signals. Cross-interference between the positioning signals is reduced by tuning the remote receiver to a frequency of a selected signal of the two positioning signals and correlating the selected signal with a reference pseudorandom ranging signal matched to a transmitted pseudorandom ranging signal of the selected signal.

TECHNICAL FIELD

The disclosure herein relates generally to positioning systems. Inparticular, this disclosure relates to a wide area positioning system.

BACKGROUND

Positioning systems like Global Positioning System (GPS) have been inuse for many years. In poor signal conditions, however, theseconventional positioning system can have degraded performance.

INCORPORATION BY REFERENCE

Each patent, patent application, and/or publication mentioned in thisspecification is herein incorporated by reference in its entirety to thesame extent as if each individual patent, patent application, and/orpublication was specifically and individually indicated to beincorporated by reference.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a wide area positioning system, under anembodiment.

FIG. 2 shows an example cell organization including multiple groups ofcells with each group being a seven-cell group, under an embodiment.

FIG. 3 shows an example cell organization using a single maximal lengthcode used with a three-group repeat pattern, under an embodiment.

FIG. 4 shows an example configuration comprising three receivers locatedmidway between transmitters emitting during slot 1, under an embodiment.

FIGS. 5A and 5B show plots of coherent integration rejection versuscarrier frequency offsets (modulo frame rate), under an embodiment.

FIG. 6 shows a table detailing performance comparisons of various cellconfigurations, under an embodiment.

FIG. 7 shows a table of cross-correlation at 0 lag offset for 7G/7F and1M/7F configurations, under an embodiment.

FIG. 8 shows a plot of worst case coherent integration gain by frameintegration versus differential velocity between two transmitters, underan embodiment.

FIG. 9 shows the seven distinct permutations of PN Codes, under anembodiment.

FIG. 10 shows a preferential Gold Code list, based upon run length (i.e.how many consecutive phases on either side of the peak haveautocorrelation 1/1023 times the peak), under an embodiment.

FIG. 11 is a block diagram of a synchronized beacon, under anembodiment.

FIG. 12 is a block diagram of a positioning system using a repeaterconfiguration, under an embodiment.

FIG. 13 is a block diagram of a positioning system using a repeaterconfiguration, under an alternative embodiment.

FIG. 14 shows tower synchronization, under an embodiment.

FIG. 15 is a block diagram of a GPS disciplined PPS generator, under anembodiment.

FIG. 16 is a GPS disciplined oscillator, under an embodiment.

FIG. 17 shows a signal diagram for counting the time difference betweenthe PPS and the signal that enables the analog sections of thetransmitter to transmit the data, under an embodiment.

FIG. 18 is a block diagram of the differential WAPS system, under anembodiment.

FIG. 19 shows common view time transfer, under an embodiment.

FIG. 20 shows the two-way time transfer, under an embodiment.

FIG. 21 is a block diagram of a receiver unit, under an embodiment.

FIG. 22 is a block diagram of an RF module, under an embodiment.

FIG. 23 shows signal up-conversion and/or down-conversion, under anembodiment.

FIG. 24 is a block diagram of a receiver system having multiple receivechains in which one of the receive chains can be used temporarily forreceiving and processing WAPS signals, under an embodiment.

FIG. 25 is a block diagram showing clock sharing in a positioningsystem, under an embodiment.

FIG. 26 is a block diagram of assistance transfer from WAPS to GNSSreceiver, under an embodiment.

FIG. 27 is a block diagram showing transfer of aiding information fromthe GNSS receiver to the WAPS receiver, under an embodiment.

FIG. 28 is an example configuration in which WAPS assistance informationis provided from a WAPS server, under an embodiment.

FIG. 29 is a flow diagram for estimating an earliest arriving path inh[n], under an embodiment.

FIG. 30 is a flow diagram for estimating reference correlation function,under an embodiment.

FIG. 31 is a flow diagram for estimating noise sub-space, under anembodiment.

FIG. 32 is a flow diagram for estimating noise sub-space, under analternative embodiment.

FIG. 33 is a flow diagram for estimating noise sub-space, under anotheralternative embodiment.

FIG. 34 is a flow diagram for estimating noise sub-space, under yetanother alternative embodiment.

FIG. 35 is a flow diagram for estimating noise sub-space, under stillanother alternative embodiment.

FIG. 36 is a block diagram of a reference elevation pressure system,under an embodiment.

FIG. 37 is a block diagram of the WAPS integrating the referenceelevation pressure system, under an embodiment.

FIG. 38 is a block diagram of hybrid position estimation using rangemeasurements from various systems, under an embodiment.

FIG. 39 is a block diagram of hybrid position estimation using positionestimates from various systems, under an embodiment.

FIG. 40 is a block diagram of hybrid position estimation using acombination of range and position estimates from various systems, underan embodiment.

FIG. 41 is a flow diagram for determining a hybrid position solution inwhich position/velocity estimates from the WAPS/GNSS systems are fedback to help calibrate the drifting bias of the sensors at times whenthe quality of the GNSS/WAPS position and/or velocity estimates aregood, under an embodiment.

FIG. 42 is a flow diagram for determining a hybrid position solution inwhich sensor parameters (such as bias, scale and drift) are estimated aspart of the position/velocity computation in the GNSS and/or WAPS unitswithout need for explicit feedback, under an embodiment.

FIG. 43 is a flow diagram for determining a hybrid position solution inwhich sensor calibration is separated from the individual positioncomputation units, under an embodiment.

FIG. 44 is a flow diagram for determining a hybrid position solution inwhich the sensor parameter estimation is done as part of the state ofthe individual position computation units, under an embodiment.

FIG. 45 shows the exchange of information between the WAPS and othersystems, under an embodiment.

FIG. 46 is a block diagram showing exchange of location, frequency andtime estimates between FM receiver and WAPS receiver, under anembodiment.

FIG. 47 is a block diagram showing exchange of location, time andfrequency estimates between WLAN/BT transceiver and WAPS Receiver, underan embodiment.

FIG. 48 is a block diagram showing exchange of location, time andfrequency estimates between cellular transceiver and WAPS receiver,under an embodiment.

FIG. 49 shows a parallel complex correlator architecture, under anembodiment.

FIG. 50 shows a 32-bit shift register implementation derived from two16-bit shift register primitives with parallel random access readcapabilities, under an embodiment.

FIG. 51 shows shift operation and readout operation rate, under anembodiment.

FIG. 52 shows a structure for an adder tree that implements a 1023×n-bitadder, under an embodiment.

FIG. 53 is a block diagram of session key setup, under an embodiment.

FIG. 54 is a flow diagram for encryption, under an embodiment.

FIG. 55 is a block diagram of the security architecture for encryption,under an alternative embodiment.

DETAILED DESCRIPTION

Systems and methods are described for determining the position of areceiver. The positioning system of an embodiment comprises atransmitter network including transmitters that broadcast positioningsignals. The positioning system comprises a remote receiver thatacquires and tracks the positioning signals and/or satellite signals.The satellite signals are signals of a satellite-based positioningsystem. A first mode of the remote receiver uses terminal-basedpositioning in which the remote receiver computes a position using thepositioning signals and/or the satellite signals. The positioning systemcomprises a server coupled to the remote receiver. A second operatingmode of the remote receiver comprises network-based positioning in whichthe server computes a position of the remote receiver from thepositioning signals and/or satellite signals, where the remote receiverreceives and transfers to the server the positioning signals and/orsatellite signals.

A method of determining position of an embodiment comprises receiving ata remote receiver at least one of positioning signals and satellitesignals. The positioning signals are received from a transmitter networkcomprising a plurality of transmitters. The satellite signals arereceived from a satellite-based positioning system. The method comprisesdetermining a position of the remote receiver using one ofterminal-based positioning and network based positioning. Theterminal-based positioning comprises computing a position of the remotereceiver at the remote receiver using at least one of the positioningsignals and the satellite signals. The network-based positioningcomprises computing a position of the remote receiver at a remote serverusing at least one of the positioning signals and the satellite signals.

A position location system is described that comprises transmitters thatbroadcast positioning signals. Each broadcasted positioning signalcomprises a pseudorandom ranging signal. The position location systemincludes a remote receiver that acquires and measures the time ofarrival of the positioning signals received at the remote receiver.During an interval of time, at least two positioning signals aretransmitted concurrently by the transmitters and received concurrentlyat the remote receiver. The two positioning signals have carrierfrequencies offset from one another by an offset that is less thanapproximately twenty-five percent of the bandwidth of each positioningsignal of the two positioning signals. Cross-interference between thepositioning signals is reduced by tuning the remote receiver to afrequency of a selected signal of the two positioning signals andcorrelating the selected signal with a reference pseudorandom rangingsignal matched to a transmitted pseudorandom ranging signal of theselected signal.

In the following description, numerous specific details are introducedto provide a thorough understanding of, and enabling description for,the systems and methods described. One skilled in the relevant art,however, will recognize that these embodiments can be practiced withoutone or more of the specific details, or with other components, systems,etc. In other instances, well known structures or operations are notshown, or are not described in detail, to avoid obscuring aspects of thedisclosed embodiments.

FIG. 1 is a block diagram of a positioning system, under an embodiment.The positioning system, also referred to herein as the wide areapositioning system (WAPS), or “system”, includes a network ofsynchronized beacons, receiver units that acquire and track the beaconsand/or Global Positioning System (GPS) satellites and optionally have alocation computation engine, and a server that comprises an index of thetransmitting beacons (e.g. towers with transmitters). The WAPS alsoincludes a billing interface, a proprietary encryption algorithm, andoptionally a location computation engine. The system operates in thelicensed/unlicensed bands of operation and transmits a proprietarywaveform for the purposes of location and navigation purposes. The WAPSsystem can be used alone, in conjunction with other positioning systemsfor better location solution, or to aid other positioning systems. Inthe context herein, a positioning system includes a system thatlocalizes one or more of latitude, longitude and altitude coordinates.

In the description herein, reference to the term “GPS” is in the broadersense of GNSS (Global Navigation Satellite System). GNSS as used hereinmay include other existing satellite positioning systems such as Glonassas well as future positioning systems such as Galileo andCompass/Beidou, to name a few.

Good performance of WAPS, when the systems are operating in a relativelysmall area, may be achieved by use of time division multiplexing (TDMA).In TDMA the transmissions from different beacons are distinguished fromone another by transmitting in different time slots. A multiplicity oftime slots (plus, optionally, auxiliary information, such a syncinformation) are generally arranged into a time multiplexing frame andoften (although not always) a beacon transmits in one or more time slotsper multiplexing frame. TDMA is efficient when a small number of timeslots (e.g., 10) are allocated per second for transmission. Whenoperating in a larger geographical area, however, unless a relativelylarge number of slots are allocated (e.g. 50 to 100), it can be the casethat the transmission from multiple towers will simultaneously bereceived by users. In fact it is highly probable that a receiver willreceive at least two concurrent transmissions from different towers ortransmitters, and these concurrent transmissions are to be distinguishedfrom one another by additional coding methods. Thus, such a modifiedsystem will no longer be a TDMA system, but a hybrid systemincorporating TDMA and additional multiplexing methods.

The additional multiplexing methods of an embodiment may include codedivision multiplexing (CDMA) in which different beacons are assigneddifferent pseudorandom (PN) spreading codes, with good cross correlationproperties from one to another. Examples of such PN codes are Goldcodes, which are utilized in GPS and in many other communicationssystems. Alternatively, or additionally, the multiplexing method mayinclude a method referred to herein as “frequency offset multiplexing”(FOM) in which small carrier frequency shifts are used to distinguishthe transmissions from different beacons. In an embodiment, somecombination of TDMA, CDMA and/or FOM are used to distinguishtransmissions from beacons that may be concurrently received by apositioning receiver.

It should be noted that the nonrepeating period of a pseudorandomspreading code is called the PN frame period and the nonrepeatingsequence is called the PN frame. This is to be distinguished from thetime multiplexing frame associated with TDMA described above, especiallywhen CDMA and TDMA are combined into hybrid systems. As an example, asystem may use 100 PN frames per time slot and 10 time slots per (time)multiplexing frame. In this case the time multiplexing frame periodequals 1000 PN frame periods. In the following description the termsmultiplexing frame and PN frame are used to distinguish the TDMA and PNframes. When the context is clear the terms “PN” and “multiplexing” maybe deleted when referring to frames. It should be noted that in WAPS, ascompared to multiple access cellular communication systems, there is aneed for a positioning receiver to receive and measure arrival times ofsignals from a multiplicity of transmitters. In fact, there is a need toreceive energy from four or more geographically spread beacons. In manyenvironments, such as suburban and urban, signal blockage andattenuation result in the received power levels from these sources beingspread over a high dynamic range, perhaps 40 dB or more. This places amuch greater constraint on the ability of a positioning receiver todistinguish received signals from one another. Hence there is a need fora positioning receiver operating in such an environment to receive andprocess signals received over a large dynamic range. Furthermore, suchreceivers also detect and process signals received from a large numberof beacons concurrently.

Another consideration concerns the effects of cross-interference uponposition location accuracy. In cellular communications systems a primaryconcern is demodulating data streams with low probability of error.Through the use of error correction coding, the effects of aninterfering signal upon a desired signal are minimized. However for WAPSsystems the interfering signal not only affects data but reduces theaccuracy of the position measurement, so there is a need to reduce theamount of cross-interference. Following interference removal, it isdesirable that the remaining signal of interest have energy 30 dB ormore relative to background noise and residual interference. This allowsaccurate ranging measurements to be made, particularly in multipathenvironments. No such constraint typically exists for cellularcommunications systems.

Examples herein show that a number of beacons in excess of 50 may berequired for detection and processing by positioning receivers operatingin an urban or wide area environment. As indicated above, if pure TDMAwere used to accomplish this, a large number of time slots, e.g. 50 ormore, would be required to serve a large geographical area. Such a largenumber of time slots would have various negative consequences. Forexample, each beacon must send data including its position and varioustiming corrections. A large number of time slots results in a very longoverall frame period needed to receive all requisite data. If data issent at a high rate to overcome this issue, then the system sensitivitysuffers. The hybrid multiplexing methods described herein overcome theseproblems. This is because only a small number of time slots are used,but this results in positioning receivers concurrently receiving signalsfrom multiple beacons. The hybrid multiplexing methods described hereinprovide the signal separation capability to distinguish theseconcurrently received signals.

In order to clearly describe the concepts of the embodiments herein, aparticular configuration of beacons, or transmitters, each centered in ahexagonal-shaped geographical region is provided herein. The embodimentsdescribed herein are not limited to this configuration, but aredemonstrated with clarity through this example. In particular thedescription herein assumes that a basic TDMA group is a seven-cell“group” arranged in a hexagonal pattern, and each group utilizes 7 timeslots. In addition it is assumed that each transmitter utilizes PN codesof length 1023 with frame period 1 msec. Again, this limitation isintroduced only for this example, and other PN code lengths and frameperiods are equally applicable.

FIG. 2 shows an example cell organization 200 including numerous groups(e.g., B, G, N, P, R, W, Y) of cells or transmitters with each groupbeing a seven-cell group, under an embodiment. A particular group, sayone marked with W, together with six similar groups surrounding it (eachwith a different letter nomenclature e.g., R, B, P, Y, N, G) is termed a“supergroup.” An exemplary TDMA/CDMA configuration uses seven (7) timeslots and seven (7) PN Codes such that each seven-cell group may beassigned one Gold Code and the numbers shown in each cell representdifferent slots. The assigned Gold Code differs from one group to thenext in a supergroup. Hence, in this example configuration, only sevencodes are required to provide a unique slot/code pair to each cell inthe supergroup, which in this example contains a total of 49 cells. Thedistance between cells having the same code and slot is approximatelyseven cell widths. This configuration is referred to as 1G/7G toindicate that each group uses only one Gold code and that the supergroupuses seven (7) total Gold codes.

In an alternative configuration each of the seven (7) groups making upthe supergroup are assigned a different frequency offset (typically afew kHz). If this is used in conjunction with the 1G/7G system describedabove, it is referred to as 1G/7G-7F. Hence in this case differentgroups are distinguished not only by having a different assigned PN, butalso a different frequency offset. As described herein, the use offrequency offsets substantially improves cross interference rejection.

In yet another alternative configuration, referred to herein as 1G/7F,only one PN code is used for all cells in a supergroup. Each cell in agroup (e.g., seven cells) is distinguished by a separate time slot andeach group is distinguished from one another by having a differentfrequency offset.

In still another alternative embodiment, each cell in a group isassigned a different PN code, but different groups utilize the same setof seven (7) PN codes. Different groups also use different frequencyoffsets. This configuration is referred to as 7G/7F.

In a further alternative configuration each cell in a supergroup isassigned a unique Gold code. Each group is further distinguished fromone another via a different frequency offset. This configuration isreferred to as 7G/7G-7F.

The various configurations above provide various degrees ofcross-interference performance. In addition the different configurationshave implications in terms of signal acquisition methodology and time,as well as system complexity. A performance comparison of some of theseconfigurations is described herein with reference to the table of FIG.6. Note that the acquisition complexity and time is proportional to theproduct of the total number of codes and total number of frequencies.

Although Gold codes were used as PN codes in the above example, othercodes are possible. For example, an embodiment includes a codecomprising a single maximal length PN sequence (e.g., the first of thetwo maximal length sequences used to form a Gold code). The codes aredistinguished within a cell group by the transmit slot number andbetween cell groups by the offset frequency. This is a variation of the1G/7F system described above, and is referred to herein as 1M/7F. Thesecodes have relatively better cross-correlation properties than similarconfigurations using Gold Codes (by approximately 5 to 6 dB).

FIG. 3 shows an example cell organization 300 using a single maximallength code used with a three-group (e.g., B, R, W) repeat pattern,under an embodiment. Each seven-cell group of this configuration 300 isassigned a maximal length code with a given frequency offset (out of aset of three offsets) and in each cell group the numbers shown representdifferent slots. This configuration is referred to herein as 1M/3F,where the M specifies “maximal length” code, as compared to the prior“G” for Gold code.

Each cellular layout embodiment may be characterized by at least twomeasures of performance. The first measure of performance is the ratio(R) of the distance between transmitters using identical transmissionparameters (e.g. slot number, code number, frequency offset and codephase) and the cell radius. The gain associated with R is R^(3.5),assuming a 3.5 loss exponent, and this provides an indication of howmuch rejection to expect, based upon geometry, for a distant transmitterrelative to a nearby transmitter. Different loss exponents may be usedto model different signaling environments (e.g. urban, suburban, rural,etc.); however, for simplicity of illustration only a 3.5 loss exponentis used herein. An approximate 40 dB gain, measured at a particularcell's radius, generally provides adequate margin in most situations,accounting for other factors, such as building blockage, etc. Thecellular configuration 200 described above with reference to FIG. 2 hasa (minimum) repeat ratio of 13.8, implying a rejection of 13.8^(3.5), or39.9 dB. Note that this does not mean that cross-interference rejectionwill be at least 39.9 dB, but does mean that a distant cell will beattenuated by this number relative to a nearby cell (i.e. one atdistance equal to cell radius) having the same multiplexing parameters.The multiplexing methods themselves have the burden of crossinterference rejection among cells by assignment of differentmultiplexing parameters, when signals are received from cells atcomparable distances from a receiver.

The second measure of performance is referred to herein as the “straddlerejection.” Assuming that a receiver is midway, or near midway, betweentwo transmitters occupying the same time slot, which is a commoncondition, the ability to process one or the other of the receivedsignals then depends upon the rejection provided by the multiplexingmethod being employed. FIG. 4 shows an example configuration 400comprising three receivers 401-403 (small black circles) positionedmidway between transmitters emitting during slot 1, under an embodiment.The receivers 401-403 are at the point closest to the two transmitters,such that receiver 401 is at the point closest to the slot 1transmitters of cell groups N and W, receiver 402 is at the pointclosest to the slot 1 transmitters of cell groups G and W, and receiver403 is at the point closest to the slot 1 transmitters of cell groups Rand W. A perpendicular line (“Equidistant Path”) indicates theequidistant trajectory, in the latter case

The receiver 402 located on the line between cell 3 of cell group W andcell 6 of cell group G is located a distance of approximately 2.55 cellradii from either of the slot 1 transmitters of cell groups W and G. Areceiver located at 402 will in an unobstructed environment typicallysee the strongest signals from cells 3 and 4 of group W and cells 6 and7 of group G. The distance to these cells are 1, 1.78, 1 and 1.78,respectively. Thus, signals received from cell 1 of W and cell 1 of G,at distance 2.55, are ideally only attenuated between 5 and 14 dBrelative to the nearby cells. Therefore, the signals from thesetransmitters are generally observable and comparable in signal strengthto at least two of the four nearest transmitters. Furthermore, thereceived signal strengths corresponding to these two transmitters may bequite comparable due to their equal distance from 402. Accordingly theymay be critical in obtaining a position fix, especially in blockagesituations. Consequently, it is desirable that the received signals beuncorrelated following signal processing.

For Gold Codes, the correlation rejection between such equidistancecells, the “straddle rejection,” is approximately 24 dB, and can be lessif Doppler is present. For a maximal length code where different cellgroups transmit at different frequencies, spaced by a multiple of theframe rate, this rejection is 30 dB. In order to achieve additionalrejection, the signal processing of an embodiment may take advantage ofthe fact that coherent processing may be performed over a period of timeequal to a multiplicity of PN frame periods, as described in detailbelow. It is shown below that frequency spacing the groups at integralmultiples of the frame rate does not allow gain through coherentaddition of multiple frames. However, certain integer plus fractionalspacing does provide substantial gain. Therefore, integer plusfractional spacing can improve the straddle rejection to levels of 40 dBand beyond. The gains through coherent integration over multiple framesare described below.

Coherent integration across multiple PN frames can reduce thecross-correlation between two codes if their carrier frequencies aredifferent. However, this should be considered in light of the fact thathaving different carriers typically yields somewhat higher crosscorrelation per PN frame. The summation of a number M of PN frameseffectively acts as a filter for a signal having frequency δf relativeto that of a desired signal. The amplitude response of this filter isgiven by

$\begin{matrix}{{A(f)} = {{{\sum\limits_{k = 0}^{M - 1}\;{\exp\left( {j\; 2\pi\; k\;\delta\;{fT}_{f}} \right)}}} = {\frac{\sin\left( {M\;{\pi\delta}\;{fT}_{f}} \right)}{M\;{\sin\left( {{\pi\delta}\;{fT}_{f}} \right)}}}}} & (1)\end{matrix}$Equation (1) is periodic in frequency with period 1/T_(f), where T_(f)is the PN frame period, and hence the integration reduction need only beconsidered over the region [0,1/T_(f)].

The overall crosstalk reduction is a product of the reduction associatedwith PN codes and that associated with the coherent integration overmultiple frames. In order to understand this crosstalk reduction,consider that a receiver is receiving a PN signal from a transmitter ina cell with PN code p(t) and frequency f₁ and also a PN signal fromanother transmitter in a different cell with PN code q (t) and frequencyf₂. The codes p and q may be the same, as in the above example, or maybe different. Then if the receiver is hypothesizing the first signal, itwill correlate the received signal energy with a replica of p(t). Thecrosstalk due to the presence of q(t) may be shown to be:

$\begin{matrix}{{\int_{0}^{{MT}_{f}}{{p(t)}{\exp\left( {{j\; 2\pi\; f_{1}t} + {j\;\theta}} \right)}q*\left( {t - \tau} \right){\exp\left( {{{- j}\; 2\pi\; f_{2}t} - {j\;\varphi} + {j\; 2\pi\; f_{2}\tau}} \right)}{dt}}} = {C\frac{\sin\left( {{\pi\left( {f_{1} - f_{2}} \right)}{MT}_{f}} \right)}{M\;{\sin\left( {{\pi\left( {f_{1} - f_{2}} \right)}T_{f}} \right)}}{\int_{0}^{T_{f}}{{p(t)}q*\left( {t - \tau} \right){\exp\left( {j\; 2{\pi\left( {f_{1} - f_{2}} \right)}t} \right)}{dt}}}}} & (2)\end{matrix}$where the correlation is assumed to be done over a period of time equalto a number M of PN frames (M=7 in the above example) each of durationT_(f). Here θ and ϕ are assumed reference and carrier phase angles and τrepresents the time offset between the frame boundaries of the referenceand received (crosstalk) signal. In equation (1) the quantity C is acomplex, constant magnitude term that is a function of θ, ϕ, τ, f₁, f₂,M and T_(f). The term within the integral is the circularcrosscorrelation between (one frame of) the two PN codes, including thefrequency difference f₁-f₂. It should be noted that thiscrosscorrelation rejection level is typically similar in value whetheror not p(t) and q(t) are the same as long as f₁-f₂ is somewhat greaterthan the frame rate. The term prior to the integral, neglecting theconstant C, is an additional rejection due to correlation over multipleframe periods (here assumed 7), and has magnitude equivalent to equation(1), using the identification δf=f₂−f₁. Good choices of δf produce thebest crosscorrelation rejection under a variety of situations, asdescribed in detail below.

When selecting the set of frequency offsets, they can be selected suchthat they are multiples of a minimum offset, say δf₀. Then, allfrequency differences will also be a multiple of this minimum. Asdescribed herein, this allows a configuration in which thecross-correlation rejection will be optimized for all pairs of signalswhich utilize different offsets from one another. Furthermore, choosingδf to be large will reduce any ambiguity that may result from thepresence of motion related Doppler shifts.

A good choice of offsets is the set:0,k ₀ R+R/Q,2k ₀ R+2R/Q,3k ₀ R+3R/Q . . . ,(Q−1)k ₀ R+(Q−1)R/Q  (3)where R is the frame rate, k₀ is a small integer (preferably two orgreater), and Q is an integer equal to the number of offsets (including0). If Q is chosen to be M, the number of frames coherently integratedprovides excellent cross-correlation results, particularly for lowDoppler shifts. Note that if another offset were used in this list itwould be Qk₀R+R. But this is a multiple of the frame rate R, and hencefrom the periodicity of (1), it has no frame integration rejection withrespect to offset 0.

FIGS. 5A and 5B show plots 500 and 501 of coherent integration rejectionversus frequency offsets (modulo frame rate), under an embodiment. Forplot 501, Q=M, and is selected to be seven (7). Shown on plot 501 arethe fractional locations (asterisks) indicating equal frequency offsetsthat may be assigned to each cell of the seven-cell group describedherein. The first cell is assumed to have 0 frequency offset. so, forexample, if the integral part of the frequency offset is a multiple of2*frame rate, the frequency offsets for the cells of the seven-cellgroup may be chosen to be 0, 2+ 1/7, 4+ 2/7, 6+ 3/7, 8+ 4/7, 10+ 5/7 and12+ 6/7, where each of these offsets is multiplied by the frame rate(e.g., for 1 kHz frame rate, frequency offset is 0, 2+ 1/7 kHz, 4+ 2/7kHz, etc.). In plot 501, by choosing M to be equal to the number of cellgroups in a supergroup, zero cross-correlation can ideally be achievedbetween any two transmitters in the supergroup. This is the situationshown in plot 501 in which the “asterisks” represent the possiblefrequency differences between transmitters in one group versus another,within the supergroup. The x-axis may be interpreted as the (fractionalpart of the) frequency difference corresponding to two transmitters asobserved by a receiver. It is noted that the received frequencydifference will in general be located at the nulls in plot 501 whenthere is zero Doppler (when the receiver is undergoing little or nomotion, such as in pedestrian situations). By contrast, in 500, Q isselected to be seven (7), but the number of frames integrated M is six(6). The location of the asterisks shows that such a frequencyassignment leads to cross correlation reduction of only around 15.6 dB,rather than the infinite reduction for the case Q=M=7. Nevertheless,such a reduction is substantial. For M very large, substantial reductionmay be obtained for a variety of values of Q. Such a situation isadvantageous in allowing a large number of frequency offsets with goodcross correlation reduction, or, alternatively, it may minimize thedeleterious effects of Doppler shifts, as discussed. For example, if thenumber of frames coherently integrated were 50, substantial crosscorrelation reduction (in the absence of Doppler) could be realized withQ as large as 50. Conversely, if Q is left at a value of seven (7) withthis integration time, a differential Doppler of nearly 127 Hz can betolerated while realizing at least 13 dB cross correlation rejectionbetween any two received signals with different frequency assignments.

In situations in which the receiver is undergoing appreciable motion,the result will be different Doppler shifts between received signals andthe relative frequencies will change. For example, the locations of theasterisks on plot 501 can move slightly to the left and right. At lowvelocity, such as at walking speeds, the degradation due to such Dopplershifts is small. At very high velocity, the advantage of coherentintegration can be lost for certain pairs of transmitters.

In terrestrial situations significant reduction in integration gain dueto Doppler effects may occur when the assigned frequency differencesbetween two receivers is the minimal nonzero number, e.g., 2 1/7 kHz inthe above example or the maximal number 12 6/7 kHz. In other situations,for this example, the gain will be at least equal to the maximumsidelobe level in plot 501, or approximately 12.5 dB. This is asubstantial gain. The probability of significant deterioration is foundby considering the probability that two cell sites have relativefrequency offsets that are the smallest and largest possible (assumingthey are nonidentical) and that the differential Doppler of signalsreceived by a receiver from these sites has the correct sign. For thecase of M=Q=7, with high Doppler (for example, fast moving receivers)the probability that the coherent integration gain is less than 12.5 dBis less than 16.7%.

When using a maximal length PN sequence instead of a Gold Code, thecross-correlation rejection (ignoring coherent gain integration) whencompared to another identical code, offset in frequency by a multiple ofthe frame rate, is almost exactly the square root of the sequencelength, as described in detail below. For a sequence of length 1023 thisamounts to 30.1 dB. Thus, this is approximately 6 dB better than twodifferent Gold Codes with zero frequency offset.

Consider the case of a constant amplitude waveform r(t), which isperiodic over T_(f) and includes a maximal length sequence s(n), n=0, .. . , L−1 (typically L=1023). Then for q (modulo the code length) anynonzero integer, the product s(n)×s(n+q) is a phase shift of the maximallength sequence. Furthermore, due to the impulsive nature of thecircular correlation property of the maximal length code, the (circular)spectrum of s is constant in magnitude (except at DC where it is nearlyzero). The result is that when the cross correlation of r(t) is computedwith a frequency shifted version of r(t), having a frequency shift thatis a multiple of the frame rate, a constant magnitude function isproduced. More precisely,

$\begin{matrix}{{{{\int_{0}^{T_{f}}{{r(t)}{r\left( {t - {qt}_{c}} \right)}e^{j\; 2\pi\;{ft}}{dt}}}} = {{{\int_{0}^{T_{f}}{{r\left( {t - {pt}_{c}} \right)}e^{j\; 2\pi\;{ft}}{dt}}}} = C}},{f = {d/T_{f}}},{q \neq 0}} & (4)\end{matrix}$where q is an integer, t_(c) is the chip duration, p is an integer, andd is a small nonzero integer (if d/T_(f) is large the chip shape willcause (4) to roll off vs. frequency). Also, it is assumed that the timeshift of r is actually a circular rotation. Here C is a constant whichis approximately the square root of correlation peak obtained for f=0.Thus for a 1023 length sequence the cross-correlation is uniform inmagnitude (except at q=0) where it is zero. Thus the cross-correlationrejection, in dB, is 20 log₁₀(1/sqrt(1023))=−30.1 dB. This follows fromParceval's theorem, or from conservation of energy.

The above is precise for a frequency shift f which is an integermultiple of the frame rate. That is, the Fourier transform propertydescribed above actually applies only to the Discrete Fourier Transform(DFT). For (integer plus) fractional differences, the worst casecross-correlation rejection can be up to 4.5 dB worse, depending uponthe frequency shift. This is reflected in table 600 described hereinwith reference to FIG. 6. When q=0, the cross-correlation gain is poorerthan at other lags. Equation 2 shows that for this case thecross-correlation gain is completely determined by the integral of asinusoid. Choosing large frequency offsets avoids this problem, at theexpense of increased signaling bandwidth. The data of table 600 showsthat at 0 lag this correlation increase can be almost 8 dB greater thanat other lags, for the case of frequency offsets multiples of 2 1/7times the frame rate. Using multiples of 3 1/7 times the frame rateimproves the correlation gain at 0 lag by 3 dB, and using multiples of 41/7 times the frame rate improves the correlation gain by yet another 2dB. Note that the poorer performance at 0 lag applies not only to themaximal length sequence situation, but also to the cases 7G/7F sincedifferent groups of a supergroup will have cells whose transmitters usethe same PN, only being differentiated by frequency offset.

This (zero lag performance) issue can be avoided by shifting (moreprecisely rotating) the PN phase for each cellular group. For example,if there are a total of seven cellular groups (of seven cells each),then each cellular group would use a different frequency offset (e.g. amultiple of (2+ 1/7)/T_(f)) and a different PN phase which for the caseillustrated previously may be chosen to be a multiple of the PN lengthdivided (approximately) by seven (7). Another method to avoid the zerolag issue, while only using seven (7) PN codes, is to permute the codesrelative to slot numbers from one group to the next. This is a variationof 7G/7F, which we might term 7G/P-7F. This is further described byexample below.

FIG. 6 shows a table 600 detailing performance comparisons of variouscell configurations, under an embodiment. FIG. 7 shows a table 700 ofcross-correlation levels at 0 lag offset for 7G/7F and 1M/7Fconfigurations, under an embodiment.

The configurations shown in table 600 have repeat ratio 13.8, assuming aseven-cell hexagonal configuration per group and seven-groupconfiguration per supergroup; frequency offsets are multiples of 2 1/7times frame rate. Computation of code rejection (at 0 Doppler) in table600 for configurations 1G/7G-7F and 7G/7F used the first seven (7) Goldcodes and searched over all pairs of codes and six (6) frequencyoffsets. For each pair of codes the highest cross correlation peak wasfound over all code phases and frequency offsets. This was consideredthe correlation gain for each pair of codes. For these cases, when arange is shown (for example 19.9-23.5), the numbers correspond topoorest cross correlation gain over all code pairs to best crosscorrelation gain over all code pairs. These values many change a littlewith different code selection. The code rejection range shown in table600 for configurations of 7G/7G-7F corresponds to finding the highestcross-correlation peak versus code phase and frequency for each pair ofcodes over a set of 49 codes, and then showing the correlation gainrange associated with such peaks.

Referring to the code rejection data shown in table 600 forconfigurations 7G/7F and 1M/7F, the first number only corresponds torelative code phase of zero between pairs of codes and for worst casefrequency offset; the first number can be improved through use of anintegral part of frequency offset greater than two (2). This worst caseoccurs when the two codes themselves are the same. The second set ofnumbers is the correlation gain range as described herein.

The maximal length code has feedback taps [3,10] identical to first oftwo constituent codes used to form GPS Gold codes.

The worst case frame integration gain shown in table 600 corresponds toa receiver observing a given differential velocity between the twotransmitters. The worst case is computed over all nonzero differences infrequency offset. For example the receiver may be traveling at 50 mphtowards one transmitter and 50 mph away from a second yielding a totalof differential velocity of 100 mph. The differential value 6 mphrepresents the worst case for walking speed (at most 3 mph). This worstcase situation only occurs when the transmitted frequency differences iseither 2+ 1/7 or 2+ 6/7 times the frame rate.

Table 600 provides information assuming that the set of frequencyoffsets is a multiple of 2 1/7 times the frame rate. However, consistentwith the description herein, for the 7G/7F and 1M/7F cases (see tablefootnote 4), there is a substantial degradation in the code rejectionfor 0 relative code phase (0 Doppler) case, when the PN codes comparedare the same. In this case, the correlation operation effectivelysquares the code and leaves only the difference frequency. Thisdifference frequency is then integrated over one frame to determine theeffective “code rejection.” If the difference frequency were an exactmultiple of the frame rate, then the rejection (at zero lag only) wouldbe infinite. However, the difference is a multiple of the frame rateplus a fraction of the frame rate.

If the frequency offset is δf, then the worst case cross correlation (indB) at zero lag is 20 log 10(|sin c(δf)|). This is listed in table 700where for each integer part of frequency offset the worst case wasdetermined over the fractional offsets 1/7 to 6/7.

With reference to table 600, and the 7G/7F cases described herein, theranges of rejection are 19.9 dB to 23 dB, except for the 0 lag case.From table 700, the 0 lag rejection equals 23 dB for integer frequencyoffset 4 times the frame rate. Even at three times the frame rate therejection is 20.8 dB, which is within the range of rejection for nonzerolag. The only disadvantage of the larger integral offsets is increasedtotal bandwidth. For integral offset 4, the increase in bandwidth is 246/7 kHz, as seen in table 700. Since this is only about 1.24% of thetotal signal bandwidth of 2 MHz (for 1 MHz chip rate), the effects ofthe slight shift in frequency are small. The range of center frequencieswould then vary over +/−12 3/7 kHz. Thus, either a slightly widertransmit and receive filter can be used to ensure capturing the mainlobeof the transmitted signal spectrum, or the signal can be allowed to beslightly more attenuated at the edge. At 1 MHz+/−12 3/7 kHz, the signalspectrum itself is down 38 dB, not including additional transmitterfiltering. Even more revealing, the energy in the region [1 MHz−12 3/7kHz, 1 MHz] is only 1.3×10⁻⁶ of the mainlobe energy and hence isnegligible.

Receiver velocity results in Doppler shifts which in many cases reducesthe effective processing gain due to coherent summation, as shown in thelast three columns of table 600. More pertinent is the differentialDoppler which is the difference in the Doppler of two transmitters asobserved by a receiver. At 930 MHz a speed of 60 MPH corresponds to amaximum Doppler, relative to a stationary platform, of 83.2 Hz (0.0895ppm). In principle then, the differential Doppler between the twostationary platforms can be as poor as 166.4 Hz at 60 MPH. Withreference to FIG. 5, this can move the uppermost asterisk to the peak ofthe curve at approximately 1 kHz, thus producing no frame summationgain, or it can cause the lower asterisk to move to the origin. Eachcase represents a specific direction of travel for each of the twoplatforms. The worst case situation may not be unusual, however, sincethere may be many circumstances when two transmitting towers are along aroadway on which a vehicle is traveling. The cellular groups can bearranged, however, so that the frequency offsets along major roadways donot differ by a fraction 1/7 or 6/7, thus minimizing the likelihood ofthis situation occurring.

At pedestrian walking speeds of say 3 MPH, the maximum differentialDoppler would be 8.32 Hz which represents only a small reduction inperformance as seen in table 600. FIG. 8 shows a plot 800 of worst casecoherent integration gain by frame integration versus differentialvelocity between two transmitters, when the number of frames summed is 6or 7.

With reference to FIG. 2, assume the 7G/7F system where each group ofthe same label (e.g., each B group) has seven (7) PN codes assigned toit, and the different labels (e.g., B, G, N, P, R, W, Y) representdifferent frequency offsets (e.g., seven (7) offsets). The numbers shownin each cell represent time slots. In this example configuration therepeat ratio is 13.8, at which point a transmitter exists that has thesame frequency offset, slot and PN code as another. A much larger repeatratio is achieved by permuting the seven (7) PN codes. That is, considera configuration that includes a supergroup that is group of seven (7)groups, each group comprising seven cells, along with six (6)surrounding groups each having seven (7) cells, for a total of 49 cells.Furthermore, six (6) similar supergroups surround any particularsupergroup. If the PN codes are permuted from one supergroup to the nextso that no PN code in a supergroup is transmitted in the same slot as inany of the surrounding supergroups, then the cross-correlation betweencells in adjacent supergroups will be at least reduced by the codecross-correlation rejection (19.9-23 dB, see table 600). The cells mayhave the same frequency offsets and hence may not gain additionally fromcoherent integration. In this manner the number of cells not havingidentical [time slot, frequency offset, PN code] triplets can beextended to a total of 7×49=343. The minimum repeat ratio for cellshaving identical triplets is approximately 36, thus implying a rejectionof a cell with an identical triplet of 36^(3.5), or 54.5 dB, which isaround 14.6 dB better than that achievable without the permutation ofthe PN codes. The above configuration may be referred to as 7G/7F/P,since the permutation occurs at the supergroup level. Note that this isdistinct from the 7G/P-7F case previously described in which thepermutation of PN codes occurred at the group level.

FIG. 9 shows seven distinct permutations 900 of PN Codes, appropriate tothe 7G/P-7F case, under an embodiment. These permutations 900 assumethat a particular position (e.g. top) in a 7-cell group is associatedwith a particular slot (e.g. 1) and the numbers represent a PN codeindex, and no PN number occurs twice in a slot. Another way to achievedistinct permutations is to associate a PN code with a slot for a givengroup and then assign the PN codes to other groups by a cyclic shift ofthe PN codes relative to the slot numbers. For example if PN codes 1 to7 are assigned to slots 1 to 7 respectively, in one group, then anothergroup of the supergroup may assign to slots 1 to 7 PN codes 2, 3, 4, 5,6, 7, 1. Similarly other groups would be assigned codes with indicesthat are other cyclic shifts of the 7 codes. As long as the number ofcodes utilized equals or exceeds the number of slots assigned totransmitters in a group, a supergroup may be formed with a number ofgroups equal to the number of slots such that no PN code will beconcurrently transmitted by more than one member of the supergroup. Sucha cyclic shift approach may also be used in the aforementioned 7G/7F/Pcase as well as another case termed 7G/7G-7F/P, discussed herein.

More than one multiplexing method may be used when the packet is dividedinto data segments and ranging segments, or alternatively, whenalternate packets include data and ranging information. Consider thesystem 7G/7F with frequency offsets as described above. During theranging section, assuming six (6) frames are coherently integrated, thenthe straddle rejection can be on the order of 40 dB or better. Duringthe data section, no benefit is derived from frame integration if asymbol duration is one frame. For the data section the rejection isapproximately 21-23 dB. This is adequate for supporting data, especiallysince the required SNR per symbol is only no more than 8 dB at theminimum signal level (this depends upon the type of error correctioncoding used). Thus, high data rate and the good rejection properties ofcoherent integration can be simultaneously achieved. When the receiveris undergoing high speed motion, the overall rejection in some cases maybe as poor as 24 dB even with the coherent integration. However, signallevels are expected to be stronger, making positioning easier.Furthermore, the geometry changes rapidly, ensuring a quick transitionthrough a poor cross-correlation environment.

By way of example, one embodiment of the above methods is now described.Under this embodiment a cluster of cells equal to seven (7) is used in aslotted arrangement, in accordance with the 7G/7F/P configuration. Sevenfrequency offsets (one being 0 frequency) are used to distinguish theseven (7) different groups of seven (7) cells, which make up asupergroup. The offset separation used is a multiple of (4+ 1/7)/framerate, which minimizes the correlation degradation for 0 lag. The sevendifferent supergroups are distinguished using a permutation of the seven(7) PN codes, where each group in a supergroup uses the samepermutation. High elevation transmitters may displace the multiplexingassignments corresponding to a number of adjacent cells with a singletriplet [time, frequency offset, PN code]; alternatively, one or moreparticular slots may be reserved for such transmitters.

An alternative configuration, mentioned previously, is the 7G/P-7Fconfiguration. Both frequency offset and PN code permutations are usedto distinguish the seven (7) different groups of seven (7) cells, whichmake up a supergroup. This configuration ensures that the same PN codeis not used in the same slot in any of the groups within a supergroup.The supergroups can interfere with each other in that the correspondingcells in the supergroups use the same [slot, PN code, frequency offset]triplet. However, this approach eliminates the possibly largecross-correlation at zero lag between transmitters in a supergroup,having the same PN and different frequency offset. As described herein,this limitation would otherwise have to be eliminated by choosing thefrequency offset set to be larger than otherwise necessary.

Another variation termed 7G/7G-7F/P utilizes 49 different PN codeswithin a given supergroup. Each different group within a supergrouputilizes a different offset frequency. Supergroups are distinguished bya permutation of the 49 PN codes from one supergroup to another in sucha manner that no supergroup has a cell with the same slot/frequency/PNassignment as any cell in an adjacent supergroup. This approach avoidsthe zero lag cross correlation reduction problem over the set of allcells in seven (7) adjacent supergroups.

FIG. 10 shows a preferential Gold Code list 1000, based upon run length(i.e. how many consecutive code phases on either side of the peak haveautocorrelation magnitude 1/1023 times the peak), under an embodiment.The table 1000 lists the initial fill of the shift register of thesecond PN code, as well as the delay, with the initial fillspecification being the more useful for implementation. The fill of thefirst PN code is always equal to all 1 s. The fill of the second PN codeis as specified in table 1000. The fill read from left to rightrepresents the first 10 outputs of the second PN generator. The fill isplaced in the shift register from the end of the shift register back tothe beginning. The first code has feedback taps at locations three (3)and 10 and is always assumed to have initial fill of all 1 s. The secondPN code has feedback taps (2, 3, 6, 8, 9, 10), with initial fill asprovided in table 1000. It is noted that the two individual maximallength (ML) codes used to construct the Gold codes may also beconsidered Gold codes, since they share the cross correlation propertiesassociated with the other codes of the Gold code set. If these wereincluded, they would be placed at the head of the table 1000, sincebeing ML codes they have autocorrelation functions with magnitudes1/1023 times the peak at all locations except for the peak location.

The ten Gold codes of the table 1000 were tested for theircross-correlation properties with frequency offsets that are multiplesof 4 1/7 times the frame rate. The peak of the cross-correlationfunctions over the set of the 10 codes and over the six (6) differentoffset differences ranged between −20.3 dB and −23.1 dB. This isslightly better than that found in table 600 (described above withreference to FIG. 6) which corresponds to the case of the first 7 GPScodes in order of delay between codes (and frequency offset which weremultiples of 2 1/7 times frame rate). Although the table 600 lists tenpreferred codes, the list may be continued to be as long as required (upto 1025 for length 1023 Gold codes), and may, alternatively be populatedwith other types of codes, and/or other code lengths, in order ofdescending run length.

In the description herein different transmitters in a cellular grouptypically transmit in different time slots. Similarly locatedtransmitters in different groups transmitted concurrently. However, themethods described herein, particularly those involving the offsetfrequency multiplexing, are not so limited. There may be cases, forexample, in which transmitters in adjacent cells transmit concurrently.For example, some transmitters may transmit in two (often successive)slots. In this case the system of an embodiment relies upon the PN andoffset frequency multiplexing to achieve requisite cross-correlationrejection. Transmitting in more than one slot increases the datathroughput of that transmitter. Auxiliary data, such as security orauthentication data may be sent in the secondary slot. In some cases atransmitter may be assigned a primary slot and a secondary slot, and thetransmitter might reduce its transmission level by a small amount, say 6dB to 10 dB during the secondary slot. If the secondary slot is usedprimarily to transmit data, and secondarily for ranging purposes, thenthe lower power level may be adequate. Another reason for transmissionin more than one slot is for more rapid synchronization. A receiverwould have additional opportunity for initial acquisition of signals inthis situation. Yet another reason to have the transmitter occupymultiple slots is to provide additional range and position locationmeasurements per second.

There are situations in which multiple transmitters in the vicinity ofone another will transmit identical waveforms concurrently. That is, thePN and frequency offsets plus any data may be common for multiplesignals concurrently transmitted. An example of this may occur at thebeginning of a time slot during which initial synchronization may occur.A receiver wishing to get an approximate timing will in these cases beable to achieve such timing without having to search over a space ofmultiple codes and/or frequency offsets. This is sometimes termed a“simulcast” transmission. With such a simulcast transmission it may bedesirable to use a PN code that is a maximal length PN code rather thana Gold code. As indicated above such maximal length codes have idealautocorrelation properties since their circular autocorrelationfunctions have the same minimal magnitude sidelobes. This property mayresult in improved probability of detection or reduced false alarmrates. It should be noted that a maximal length code may be implementedby a simple modification of a Gold code generator. The initial fill ispreloaded to all zeros in the linear feedback generator of one of thetwo generators that are used to generate the Gold code. This willproduce the maximal length sequence associated with the other generator.

The frequency offset multiplexing of an embodiment has a relativelysmall frequency offset between transmitters relative to the overallbandwidth of each of the transmitted signals. This ensures that thetotal bandwidth occupied by all the transmitted signals is notsubstantially larger than each individual transmitter. The examplesprovided herein used offsets that were less than 1% of the signalbandwidth. However, an embodiment herein applies to situations in whichthe difference in frequency offsets between a pair of transmitters aremuch larger, but less than the signal bandwidth. In order to conservetotal signal bandwidth, it is often desirable to keep such offsetdifferences below approximately 25% of the signal bandwidth, andcertainly less than 50% of the signal bandwidth. As an example, if 5different frequency offsets were employed and the difference betweenadjacent offsets was 25% of the signal bandwidth, then the totalpassband required would be twice the bandwidth of any of the signals.

Embodiments using larger offsets are applicable for situations in whichthe signal bandwidth is small and there is appreciable Doppler. In thesecases the larger offsets between the signals allow them to be separablein frequency even when undergoing large differential Doppler. It isnoted that traditional frequency division multiplexing methods utilizeoffsets that are at least equal to the signal bandwidths (typically muchlarger) and orthogonal frequency division multiplexing (OFDM) uses a setof carrier frequencies whose offsets, relative to one another, areapproximately half the bandwidth associated with each carrier (asmeasured by the null-to-null passband width).

In another embodiment, wideband, non-pseudorandom ranging signals areused in substitution for the pseudorandom ranging signals describedherein. For example, one might use a set of chirp type signals forranging, with the set comprising chirp signals having different chirprates (i.e. frequency vs. time rates). The embodiments described hereinapply to this situation. For example, the use of offset frequencymultiplexing applies, and in particular equation (2) herein applies withp(t) and q(t) being wideband signals transmitted by differenttransmitters, T_(f) the nonrepeating duration of the wideband signals, Mthe number of repetitions of the signals integrated, and the otherquantities as described herein. Similarly, information symbols may betransmitted by appropriately modulating at slow rate the widebandsignals (e.g. using phase reversals).

WAPS Systems and Methods

FIG. 11 is a block diagram of a synchronized beacon, under anembodiment. With reference to FIG. 11 as well as FIG. 1, thesynchronized beacons of an embodiment, also referred to herein asbeacons, form a CDMA network, and each beacon transmits a signal inaccordance with a Pseudo Random Number (PRN) sequence with goodcross-correlation properties such as a Gold Code sequence with a datastream of embedded assistance data. Alternatively, the sequences fromeach beacon transmitter can be staggered in time into separate slots ina TDMA format.

In a terrestrial positioning system, one of the main challenges toovercome is the near-far problem wherein, at the receiver, a far-awaytransmitter will get jammed by a nearby transmitter. To address thisissue, beacons of an embodiment use a combination of CDMA, TDMAtechniques, and frequency offset techniques. Such a system is termed ahybrid multiplexing system since it is not one of these methods alone,but a combination. As an example, local transmitters may use separatetime slots (and optionally different codes (CDMA)) to alleviate thenear-far problem. Transmitters somewhat further afield would be allowedto use the same time slots while using different CDMA codes, and/orfrequency offsets. This allows wide-area scalability of the system. Thetime slotting can be deterministic for guaranteed near-far performanceor randomized to provide good average near-far performance. As indicatedherein, the carrier signal can also be offset by a small frequencydifference (for example, on the order of the Gold code repeat frequency)to improve cross-correlation performance of the codes and hence address‘near-far’ issues. When two towers use the same time slot but differentcodes, and or offset frequencies, the cross-correlation in the receivercan be further rejected by using interference cancellation of thestronger signal before detecting the weaker signal. In the hybridpositioning systems described herein sophisticated planning methods areused to assign to each transmitter combinations of time slots, CDMAcodes, and frequency offsets so as to maximize overall systemperformance. The number of combinations of these parameters is limitedin order to allow signal acquisition time by a receiver to be apractical value.

Additionally, the beacons of an embodiment can use a preamble includingassistance data or information can be used for channel estimation andForward Error Detection and/or Correction to help make the data robust.The assistance data of an embodiment includes, but is not limited to,one or more of the following: precise system time at either the risingor falling edge of a pulse, or a specified signal epoch, of thewaveform; Geocode data (Latitude, Longitude and Altitude) of the towers;geocode information about adjacent towers and index of the sequence usedby various transmitters in the area; clock timing corrections for thetransmitter (optional) and neighboring transmitters; local atmosphericcorrections (optional); relationship of WAPS timing to GNSS time(optional); indication of urban, semi-urban, rural environment to aidthe receiver in pseudorange resolution (optional); and, offset from baseindex of the PN sequence or the index to the Gold code sequence. In thetransmit data frame that is broadcast, a field may be included thatincludes information to disable a single or a set of receivers forsafety and/or license management reasons.

The transmit waveform timing of the transmissions from the differentbeacons and towers of an embodiment are synchronized to a common timingreference. Alternatively, the timing difference between thetransmissions from different towers should be known and transmitted. Theassistance data is repeated at an interval determined by the number andsize of the data blocks, with the exception of the timing message whichwill be incremented at regular intervals. The assistance data may beencrypted using an encryption algorithm. The spreading code may also beencrypted for additional security. The signal is up-converted andbroadcast at the predefined frequency. The end-to-end delay in thetransmitter is accurately calibrated to ensure that the differentialdelay between the beacons is less than approximately 3 nanoseconds.Using a differential WAPS receiver at a surveyed location listening to aset of transmitters, relative clock corrections for transmitters in thatset can be found.

The tower arrangement of an embodiment is optimized for coverage andlocation accuracy. The deployment of the towers will be arranged in sucha way as to receive signals from 3 or more towers in most of thelocations within the network and at the edge of the network, such thatthe geometric dilution of precision (GDOP) in each of these locations isless than a predetermined threshold based on the accuracy requirement.Software programs that do RF planning studies will be augmented toinclude the analysis for GDOP in and around the network. GDOP is afunction of receiver position and transmitter positions. One method ofincorporating the GDOP in the network planning is to set up anoptimization as follows. Function to be minimized is volume integral ofthe square of GDOP over the coverage volume. The volume integration iswith respect to the (x, y, z) coordinates of the receiver position. Theminimization is with respect to the n transmitter position coordinates(x₁, y₁, z₁), (x₂, y₂, z₂), (x_(n), y_(n), z_(n)) in a given coveragearea subject to the constraints that they are in the coverage volume:x_(min)<x<x_(max), y_(min)<_(Y)<y_(max) z_(min)<Z<z_(max) for i=1, . . ., n with x_(min), y_(min) and z_(min) being the lower limits and withx_(max), y_(max) and z_(max) being the upper limits of the coveragevolume. The function to be minimized can be written as

${f\left( {x_{i},y_{i},{z_{i};{i = 1}},2,{\ldots\mspace{14mu} n}} \right)} = {\underset{{x \in {({{xl},{xu}})}},{y \in {({{yl},{yu}})}},{z \in {({{zl},{zu}})}}}{\int{\int\int}}{{GDOP}^{2}\left( {x,y,z,x_{i},y_{i},{z_{i};{i = 1}},2,{\ldots\mspace{14mu} n}} \right)}}$

Additionally, the function to be minimized may be weighted according tothe importance (i.e. performance quality required) of the coverageregion R_(j).

${f\left( {x_{i},y_{i},{z_{i};{i = 1}},2,{\ldots\mspace{14mu} n}} \right)} = {\sum\limits_{j}\;{W_{j}\underset{x,y,{z \in R_{j}}}{\int{\int\int}}{{GDOP}^{2}\left( {x,y,z,x_{i},y_{i},{z_{i};{i = 1}},2,{\ldots\mspace{14mu} n}} \right)}}}$

An additional constraint on the tower coordinate locations can be basedon location of already available towers in the given area. Thecoordinatization of all coordinates can typically be done in local levelcoordinate system with average east as positive x, average north aspositive y and average vertical up as positive z. The software whichsolves the above constrained minimization problem will output optimizedtransmitter positions (x₁, y₁, z₁), (x₂, y₂, z₂), (x_(n), y_(n), z_(n))that would minimize the function ƒ.

$\arg{\min\limits_{x_{i},y_{i},{z_{i};{i = 1}},2,{\ldots\mspace{14mu} n}}\left( {f\left( {x_{i},y_{i},{z_{i};{i = 1}},2,{\ldots\mspace{14mu} n}} \right)} \right)}$

This technique can be applied for both wide area networks (like in acity) or in a local deployment (like in a mall). In one exampleconfiguration, the network of transmitters is separated by a distance ofapproximately 30 km in a triangular/hexagonal arrangement around eachmetropolitan area. Each tower can radiate via a corresponding antenna upto a maximum power in a range of approximately 20 W to 1 kW EIRP. Inanother embodiment, the towers can be localized and can transmit atpower levels as low as 1 W. The frequency bands of operation include anylicensed or unlicensed band in the radio spectrum. The transmit antennaof an embodiment includes an omni-directional antenna, or multipleantennas/arrays that can help with diversity, sectoring etc.

Adjacent towers are differentiated by using different sequences withgood cross-correlation properties to transmit or alternatively totransmit the same sequences at different times. These differentiationtechniques can be combined and applied to only a given geographicalarea. For instance the same sequences could be reused over the networksin a different geographical area.

Local towers can be placed in a given geographical area to augment thewide area network towers of an embodiment. The local towers, when used,can improve the accuracy of the positioning. The local towers may bedeployed in a campus like environment or, for public safety needs,separated by a distance in a range of few 10s of meters up to a fewkilometers.

The towers will preferably be placed on a diversity of heights (ratherthan on similar heights) to facilitate a better quality altitudeestimate from the position solution. In addition to transmitters atdifferent latitude/longitude having different heights, another method toadd height diversity to the towers is to have multiple WAPS transmitters(using different code sequences) on the same physical tower (withidentical latitude and longitude) at different heights. Note that thedifferent code sequences on the same physical tower can use the sameslots, because transmitters on the same tower do not cause a near-farproblem.

WAPS transmitters can be placed on pre-existing or new towers used forone or more other systems (such as cellular towers). WAPS transmitterdeployment costs can be minimized by sharing the same physical tower orlocation.

In order to improve performance in a localized area (such as, forexample, a warehouse or mall), additional towers can be placed in thatarea to augment the transmitters used for wide area coverage.Alternatively, to lower costs of installing full transmitters, repeaterscan be placed in the area of interest.

Note that the transmit beacon signals used for positioning discussedabove need not be transmitters built exclusively for WAPS, but can besignals from any other system which are originally synchronized in timeor systems for which synchronization is augmented through additionaltiming modules. Alternately, the signals can be from systems whoserelative synchronization can be determined through a reference receiver.These systems can be, for example, already deployed or newly deployedwith additional synchronization capability. Examples of such systems canbe broadcast systems such as digital and analog TV or MediaFlo.

When the WAPS network is configured, some transmit locations may bebetter than some others in the network (height of the beacon aboveclutter, power levels) either determined by design or by fieldmeasurements. Such beacons can be identified to the receivers eitherdirectly or indirectly or by encoding data bits which indicate the“quality” of the beacon which the receivers can then use to weight thesignal received from such beacons.

FIG. 12 is a block diagram of a positioning system using a repeaterconfiguration, under an embodiment. The repeater configuration comprisesthe following components:

1) A common WAPS receive antenna (Antenna 1)

2) An RF power amplifier and a splitter/switch connects to various WAPStransmitter antennas (Local Antennas 1-4).

3) WAPS User Receiver

Antenna1 receives, amplifies and distributes (switches) the compositesignal to Local Antennas 1-4. The switching should be done (preferably)in a manner such that there is no overlap (collision) of transmissionsfrom different repeaters at the user receiver. Collision oftransmissions can be avoided through the use of guard intervals. Theknown cable delays from the switch to the transmit antenna should becompensated either by adding delays at therepeater-amplifier-transmitter to equalize the overall delay for alllocal repeaters or by adjusting the estimated time of arrival from aparticular repeater by the cable delay at the user-receiver. When TDMAis used in the wide area WAPS network, the repeater slot switching rateis chosen such that each wide area slot (each slot will contain one widearea WAPS tower) occurs in all repeater slots. One example configurationwould use the repeater slot duration equal to a multiple of the widearea TDMA frame duration. Specifically, if the wide area TDMA frame is 1second, then the repeater slots can be integer seconds. Thisconfiguration is the simplest, but is suitable only for deployment in asmall, limited area because of requirement of RF signal distribution oncables. The user WAPS receiver uses time-difference of arrival whenlistening to repeater towers to compute position and works under astatic (or quasi static) assumption during the repeater slotting period.The fact that the transmission is from a repeater can be detectedautomatically by the fact that each WAPS tower signal shows the sametiming difference (jump) from one repeater slot to the next one.

FIG. 13 is a block diagram of a positioning system using a repeaterconfiguration, under an alternative embodiment. In this configurationeach repeater comprises a WAPS repeater-receiver and an associatedcoverage-augmentation WAPS transmitter with local antenna (which can beindoors, for example). The WAPS repeater receiver should be able toextract WAPS system timing information as well as WAPS data streamcorresponding to one wide area WAPS transmitter. The WAPS system timingand data corresponding to one wide area WAPS transmitter are passed tothe corresponding local area WAPS transmitters which can thenre-transmit the WAPS signal (for example, using a different code and thesame slot). The transmitter will include additional data in itstransmission such as latitude, longitude and altitude of the localantenna. In this configuration, the WAPS user receiver operation (rangemeasurement and position measurement) can be transparent to the factthat the signals are coming from repeaters. Note that the transmitterused in the repeater is cheaper than a full WAPS beacon in that it doesnot need to have a GNSS timing unit to extract GNSS timing.

Depending on the mode of operation of the receiver unit, eitherterminal-based positioning or network-based positioning is provided bythe system. In terminal based positioning, the receiver unit computesthe position of the user on the receiver itself. This is useful inapplications like turn-by-turn directions, geo-fencing etc. In networkbased positioning, the receiver unit receives the signals from thetowers and communicates or transmits the received signal to a server tocompute the location of the user. This is useful in applications likeE911, and asset tracking and management by a centralized server.Position computation in the server can be done in near real time orpost-processed with data from many sources (e.g., GNSS, differentialWAPS etc.) to improve accuracy at the server. The WAPS receiver can alsoprovide and obtain information from a server (similar, for example, to aSUPL Secure User PLane server) to facilitate network based positioning.

The towers of an embodiment maintain synchronization with each otherautonomously or using network-based synchronization. FIG. 14 shows towersynchronization, under an embodiment. The following parameters are usedin describing aspects of synchronization:

-   -   System transmitter time=t_(WAPS-tx)    -   Absolute time reference=t_(WAPS_abs)    -   Time Adjustment=Δ_(system=)t_(WAPS-tx)−t_(WAPS_abs)        Note that it is not essential to synchronize WAPS system time to        an absolute time reference. However, all WAPS transmitters are        synchronized to a common WAPS system time (i.e. relative timing        synchronization of all WAPS transmitter). Timing corrections of        each transmitter relative to WAPS system time (if any) should be        computed. The timing corrections should be made available to the        receivers either directly through over the air WAPS assistance        transmission or through some other communication means. The        assistance can be delivered, for example, to the WAPS receiver        through a cellular (or other) modem or through a broadcast data        from a system (such as Iridium or digital TV or MediaFlo or        broadcast channels of cellular systems). Alternatively, the        timing correction can be sent to the server and used when        computing position at the server. A description of tower        synchronization of an embodiment follows.

Under network based synchronization, the towers synchronize with eachother in a local area. The synchronization between towers generallyincludes transmission of a pulse (which can be modulated using any formof modulation onto a carrier and/or spread using a spreading code forbetter time resolution which in turn modulates a carrier) andsynchronizing to the pulse edge on the receiver, as described in detailherein.

In the autonomous synchronization mode of an embodiment, the towers aresynchronized using a local timing reference. The timing reference can beone of the following, for example: GPS receivers; highly accurate clocksources (e.g., Atomic); a local time source (e.g., GPS disciplinedclock); and, any other network of reliable clock sources. Use of signalsfrom XM satellite radio, LORAN, eLORAN, TV signals etc. which areprecisely time synchronized can be used as a coarse timing reference forthe towers. As an example in one embodiment, FIG. 15 is a block diagramof a PPS pulse source from a GPS receiver being used to discipline anaccurate/stable timing source such as a Rubidium, Caesium or a hydrogenmaster, under an embodiment. Alternatively, a GPS disciplined Rubidiumclock oscillator can be used, as shown in FIG. 16.

With reference to FIG. 15, the time constant of the PLL in the accurateclock source is set to a large enough number (e.g., in the range of0.5-2 hours) which provides for better short term stability (orequivalently, filtering of the short term GPS PPS variations) and theGPS-PPS provides for longer term stability and wider area ‘coarse’synchronization. The transmitter system continuously monitors these twoPPS pulses (from the GPS unit and from the accurate clock source) andreports any anomaly. The anomalies could be that after the two PPSsources being in lock for several hours, one of the PPS sources driftsaway from the other source by a given time-threshold determined by thetower network administrator. A third local clock source can be used todetect anomalies. In case of anomalous behavior, the PPS signal whichexhibits the correct behavior is chosen by the transmitter system andreported back to the monitoring station. In addition, the instantaneoustime difference between the PPS input and PPS output of the accuratetime source (as reported by the time source) can either be broadcast bythe transmitter or can be sent to the server to be used when postprocessing.

In the transmitter system, the time difference between the rising edgeof the PPS pulse input and the rising edge of the signal that enablesthe analog sections of the transmitter to transmit the data is measuredusing an internally generated high speed clock. FIG. 17 shows a signaldiagram for counting the time difference between the PPS and the signalthat enables the analog sections of the transmitter to transmit thedata, under an embodiment. The count that signifies that difference issent to each of the receivers as a part of the data stream. Use of ahighly stable clock reference such as a Rubidium clock (the clock isstable over hours/days) allows the system to store/transmit thiscorrection per tower on the device, just in case the device cannotmodulate the specific tower data anymore. This correction data can alsobe sent via the communication medium to the device, if there is oneavailable. The correction data from the towers can be monitored byeither reference receivers or receivers mounted on the towers thatlisten to other tower broadcasts and can be conveyed to a centralizedserver. Towers can also periodically send this count information to acentralized server which can then disseminate this information to thedevices in the vicinity of those towers through a communication link tothe devices. Alternatively, the server can pass the information fromtowers (e.g., in a locale) to neighboring towers so that thisinformation can be broadcast as assistance information for theneighboring towers. The assistance information for neighboring towersmay include position (since the towers are static) and timing correctioninformation about towers in the vicinity.

Similar to the transmitter timing correction of an embodiment, when atrue PPS is available it can be used to estimate multipath bias andprecise true range. The receiver estimates range using samples of thesignal, for example from the ADC. The receiver of an embodiment uses ahigh speed clock to determine the difference between the occurrence ofthe PPS and the first edge of the sample ADC clock. This allows therange estimated by the receiver based on the ADC samples to be correctedfor the difference between when true PPS occurs and when the ADC samplesthe data, thus allowing for estimation of the true range of the receiverto a precision better than the sample clock resolution of the ADC. Inthe context of the discussion in the paragraph above, the PPS refers toa pulse whose edge is aligned to or has known offset from a standardtiming base such as GPS pulse-per-second (PPS) timing.

In another embodiment, a wide area differential positioning system canbe used to correct for timing errors from the towers. FIG. 18 is a blockdiagram of the differential WAPS system, under an embodiment. Areference receiver (located at a pre-surveyed location) is used toreceive signals from all the towers in the vicinity. Although theprinciples of differential GPS are applied in this method, dealing withthe effects of non-line-of-sight in the terrestrial case makes itunique. The reference receiver's pseudorange (code phase) measurementsfor each tower are time-tagged and then sent to the server. The receivedcode phase-based ranges measured at the reference receiver for towers jand i can be written as follows:R _(ref) ^(j)(t)=ρ_(ref) ^(j) +c(dt _(ref) −dt ^(j))+ε_(R,ref) ^(j)R _(ref) ^(i)(t)=ρ_(ref) ^(i) +c(dt _(ref) −dt ^(i))+ε_(R,ref) ^(i)where ρ_(ref) ^(j) is the reference receiver to transmit tower jgeometric range, dt_(ref) and dt^(j) are respectively the referencereceiver and transmitter clock offsets referred to their respectiveantennas with respect to a common reference time (say, GPS time), c isthe speed of light, and ε_(R,ref) ^(j) is the measurement noise.

The differences in clock timing between the towers i and j,dt^(i)−dt^(j) are computed at the server by subtracting the twoequations above and using the known geometric ranges from referencereceiver to the transmit towers. This allows for elimination of thetiming differences between the transmitters in the rover/mobile stationmeasurements. Note that averaging over time can be used to get better(e.g., less noisy) estimates of the time difference dt^(i)−dt^(j) whenthe clocks used in the transmit towers are relatively stable.

The rover/mobile station's pseudorange measurements are also time taggedand sent to a server. The received code phase based ranges measured atthe rover/mobile station can be written as:R _(m) ^(i)(t)=ρ_(m) ^(i) +c(dt _(m) −dt ^(i))+ε_(R,m) ^(i)R _(m) ^(j)(t)=ρ_(m) ^(j) +c(dt _(m) −dt ^(j))+ε_(R,m) ^(j)By subtracting the two equations above and re-arranging, the result is(ρ_(m) ^(j)−ρ_(m) ^(i))=(R _(m) ^(j)(t)−R _(m) ^(i)(t))−c(dt ^(i) −dt^(j))+(ε_(R,m) ^(i)−ε_(R,m) ^(j)).Note that R_(m) ^(j)(t) and R_(m) ^(i)(t) are measured quantities andthe quantity dt^(i)−dt^(j) is computed from the reference receivermeasurements. Each of ρ_(ref) ^(j) and ρ_(ref) ^(j) can be written interms of the unknown coordinates of the receiver and the knowncoordinates of the transmit towers i and j. With three rangemeasurements, two range difference equations can be formed as above toobtain a two-dimensional position solution or with four rangemeasurements, three range difference equations can be formed as above toobtain a three-dimensional position. With additional measurements, aleast square solution can be used to minimize the effect of the noisequantities ε_(R,m) ^(i) and ε_(R,m) ^(j).

Alternatively, the timing difference corrections can be sent back to themobile station to correct for the errors in-situ and to facilitateposition computation at the mobile station. The differential correctioncan be applied for as many transmitters as can be viewed by both thereference and the mobile stations. This method can conceptually allowthe system to operate without tower synchronization or alternatively tocorrect for any residual clock errors in a loosely synchronized system.

Another approach is a standalone timing approach as opposed to thedifferential approach above. One way of establishing timingsynchronization is by having GPS timing receivers at each Transmit towerin a specific area receive DGPS corrections from a DGPS referencereceiver in the same area. A DGPS reference receiver installed at aknown position considers its own clock as a reference clock and findscorrections to pseudo-range measurements to the GPS satellites ittracks. The DGPS correction for a particular GPS satellite typicallycomprises total error due to satellite position and clock errors andionospheric and tropospheric delays. This total error would be the samefor any pseudo-range measurement made by other GPS receivers in theneighborhood of the DGPS reference receiver (typically with an area ofabout 100 Km radius with the DGPS receiver at the center) because lineof sight between DGPS reference receiver and GPS satellite does notchange much in direction within this neighborhood. Thus, a GPS receiverusing DGPS correction transmitted by a DGPS reference receiver for aparticular GPS satellite uses the correction to remove this total errorfrom its pseudo-range measurement for that satellite. However in theprocess it would add the DGPS reference receiver's clock bias withrespect to GPS time to its pseudo-range measurement. But, since thisclock bias is common for all DGPS pseudo-range corrections, its effecton the timing solutions of different GPS receivers would be a commonbias. But this common bias gives no relative timing errors in thetimings of different GPS receivers. In particular, if these GPSreceivers are timing GPS receivers (at known positions) then all of themget synced to the clock of DGPS reference receiver. When these GPStiming receivers drive different transmitters, the transmissions alsoget synchronized.

Instead of using corrections from a DGPS reference receiver, similarcorrections transmitted by Wide Area Augmentation System (WAAS)satellites can be used by GPS timing receivers to synchronizetransmissions of the transmitters which they drive. An advantage of WAASis that the reference time is not that of the DGPS reference system butit is the GPS time itself as maintained by the set of accurate atomicclocks.

Another approach to achieving accurate time synchronization between thetowers across a wide area is to use time transfer techniques toestablish timing between pairs of towers. One technique that can beapplied is referred to as “common view time transfer”. FIG. 19 showscommon view time transfer, under an embodiment. The GPS receivers in thetransmitters that have the view of a common satellite are used for thispurpose. Code phase and/or carrier phase measurements from each of thetowers for the satellites that are in common view are time taggedperiodically (e.g., minimum of once every second) by the GPS receiversand sent to a server where these measurements are analyzed.

The GPS code observable R_(p) ^(i) (signal emitted by satellite “i” andobserved by a receiver “p”) can be written as:R _(p) ^(i)(t)=ρ_(p) ^(i) +c(δ_(R) ^(i)+δ_(R,p) +T _(p) ^(i) +I _(p)^(i))+c(dt _(p) −dt ^(i))+ε_(R,p),where ρ_(p) ^(i), is the receiver-satellite geometric range equal to|{right arrow over (X)}_(p)−{right arrow over (X)}^(i)|, {right arrowover (X)}_(p) is the receiver antenna position at signal reception time,{right arrow over (X)}^(i) represents the satellite position at signalemission time, I_(p) ^(i) and T_(p) ^(i) are respectively theionospheric and tropospheric delays, and δ_(R) _(p) and δ_(R) ^(i) arethe receiver and satellite hardware group delays. The variable δ_(R)_(p) includes the effect of the delays within the antenna, the cableconnecting it to the receiver, and the receiver itself. Further, dt_(p)and dt^(i) are respectively the receiver and satellite clock offsetswith respect to GPS time, c is the speed of light, and ε_(R) is themeasurement noise.

The common view time transfer method computes the single difference codeobservable R_(pq) ^(i), which is the difference between code observablessimultaneously measured at two receivers (called “p” and “q”) as

$R_{pq}^{i} = {\underset{\underset{\begin{matrix}{{geometrical}\mspace{14mu}{range}} \\{difference}\end{matrix}}{︸}}{\rho_{p}^{i} - \rho_{q}^{i}} + \underset{\underset{\begin{matrix}{{time}\mspace{14mu}{difference}} \\{{between}\mspace{14mu}{clocks}}\end{matrix}}{︸}}{c\left( {{dt}_{p} - {dt}_{q}} \right)} + \underset{\underset{\begin{matrix}{{{Troposhpere}\&}{Ionosphere}} \\{{delay}\mspace{14mu}{difference}}\end{matrix}}{︸}}{{c\left( {T_{p}^{i} - T_{q}^{i}} \right)} + {c\left( {I_{p}^{i} - I_{q}^{i}} \right)}} + \underset{\underset{\begin{matrix}{{Group}\mspace{14mu}{delay}\mspace{14mu}{difference}} \\{{between}\mspace{14mu}{receivers}}\end{matrix}}{︸}}{c\left( {\delta_{R,p} - \delta_{R,q}} \right)} + \left( {ɛ_{R,p} - ɛ_{R,q}} \right)}$In calculating the single difference observable, the group delay in thesatellite as well as the clock error of the satellite gets cancelled.Also, note that in the above equation the tropospheric and ionosphericperturbations cancel (or, can be modeled, for example in cases where thereceiver separation is large). Once the group delay differences betweenthe receivers are calibrated, the desired time differencec(dt_(p)−dt_(q)) between the receiver clocks can be found from theequation. The single difference across multiple time and satellitemeasurements can be combined to further improve the quality of theestimated time difference.

In a similar manner, the single difference carrier phase equation forcommon view time transfer can be written as:

$\Phi_{pq}^{i} = {\underset{\underset{\begin{matrix}{{geometrical}\mspace{14mu}{range}} \\{difference}\end{matrix}}{︸}}{\rho_{p}^{i} - \rho_{q}^{i}} + \underset{\underset{\begin{matrix}{{time}\mspace{14mu}{difference}} \\{{between}\mspace{14mu}{clocks}}\end{matrix}}{︸}}{c\left( {{dt}_{p} - {dt}_{q}} \right)} + \underset{\underset{\begin{matrix}{{{Troposhpere}\&}{Ionosphere}} \\{{delay}\mspace{14mu}{difference}}\end{matrix}}{︸}}{{c\left( {T_{p}^{i} - T_{q}^{i}} \right)} + {c\left( {I_{p}^{i} - I_{q}^{i}} \right)}} + \underset{\underset{\begin{matrix}{{Group}\mspace{14mu}{delay}\mspace{14mu}{difference}} \\{{between}\mspace{14mu}{receivers}}\end{matrix}}{︸}}{c\left( {\delta_{\phi,p} - \delta_{\phi,q}} \right)} + \underset{\underset{\begin{matrix}{{initial}\mspace{14mu}{ambiguity}} \\{{in}\mspace{14mu}{phase}}\end{matrix}}{︸}}{\lambda\left( {\phi_{p}^{i} - \phi_{q}^{i}} \right)} + \underset{\underset{\begin{matrix}{{integer}\mspace{14mu}{ambiguity}\mspace{14mu}{in}} \\{{phase}\mspace{14mu}{measurement}}\end{matrix}}{︸}}{\lambda\left( {N_{p}^{i} - N_{q}^{i}} \right)} + {\left( {ɛ_{\phi,p} - ɛ_{\phi,q}} \right).}}$Note that since initial phase ambiguity and integer ambiguity arepresent in the above equation, the phase single difference cannot beused to determine the time transfer directly. A combined use of the codeand phase observations allows for advantage to be taken of the absoluteinformation about time difference from the codes and the preciseinformation about the evolution of time difference from the carrierphases. The error variance in the carrier phase single difference issignificantly better than the code phase single difference leading tobetter time transfer tracking.

The resulting errors per tower for a given satellite are either sentback to the tower for correction, applied at the tower, sent to thereceivers over the communication link for the additional corrections tobe done by the receiver, or sent as a broadcast message along with othertiming corrections from the tower. In specific instances, it might besuch that the measurements from the towers and the receiver arepost-processed on the server for better location accuracy. A singlechannel GPS timing receiver or a multiple channel timing receiver thatproduces C/A code measurements and/or carrier phase measurements from L1and/or L2 or from other satellite systems such as Galileo/Glonass can beused for this purpose of common view time transfer. In multiple channelsystems, information from multiple satellites in common view arecaptured at the same instant by the receivers.

An alternative mechanism in “common view time transfer” is to ensurethat different timing GPS receivers in the local area (each feeding toits corresponding transmitter) use only common satellites in theirtiming pulse derivation (e.g., one pulse per second) but no attempt ismade to correct the timing pulses to be aligned to the GPS (or UTC)second. The use of common view satellites ensure that common errors intiming pulses (such as common GPS satellite position and clock errorsand ionospheric and tropospheric delay compensation errors) pull theerrors in timing pulse by about same magnitude and relative errors intiming pulses are reduced. Since, in positioning, only relative timingerrors matter, there is no need for any server-based timing errorcorrection. However, a server can give commands to different GPSreceivers on which GPS satellites are to be used in deriving timingpulses.

An alternative method of time transfer is the “two-way time transfer”technique. FIG. 20 shows the two-way time transfer, under an embodiment.Consider two towers that are used to time against each other.Transmissions from each of the two transmitters starts on the PPS pulseand a time interval counter is started on the receive section (WAPSReceiver) of the transmit towers. The received signal is used to stopthe time interval counter on either side. The results from the timeinterval counter are sent over the data modem link to the WAPS serverwhere these results along with transmit times are compared and theerrors in timing between the two towers can be computed. This can thenbe extended to any number of towers. In this method, the relationshipbetween the counter measurements ΔT_(i) at tower i and ΔT_(j) at towerj, and the time difference dt_(ij) between the clock in i and j can berepresented asdt _(ij) =T _(i) −T _(j)=½(ΔT _(i) −ΔT _(j))+½[τ_(i) ^(Tx)+τ_(j)^(Rx))],where τ_(i) ^(Tx) & τ_(j) ^(Tx) are the transmitter delays of thetowers, and τ_(i) ^(Rx) & τ_(j) ^(Rx) are the receiver delays of towers.The time difference can be estimated once the transmitter and receiverdelays are calibrated.

In addition to the time transfer between towers, the timing of thetowers relative to GPS time can be found by the GPS timing receiversused in common view time transfer. Using the range measurement asR _(p) ^(i)(t)=ρ_(p) ^(i) +c(δ_(R) ^(i)+δ_(R,p) +T _(p) ^(i) +I _(p)^(i))+c(dt _(p) −dt ^(i))+ε_(R,p),the time correction of local clock relative to GPS time dt_(p) iscomputed, after accounting for the delay of the receiver, satelliteclock errors and ionospheric/tropospheric errors. The delay of thereceiver δ_(R,p) can be calibrated by measurement of the group delay.Information from the GPS satellite navigation message (either obtainedthrough demodulation or from a server) can be used to compute thesatellite timing correction which eliminates the effect of dt^(i) andδ_(R) ^(i). Similarly, troposphere and ionosphere delay effects areminimized using the corrections from an external model. Ionosphericcorrections can be obtained for example from WAAS messages.Alternatively, a combination of clock and ionospheric/troposphericcorrections can be obtained from RTCM DGPS corrections for thepseudorange, when available.

The offset relative to GPS time can also be sent as part of the datastream from the towers. This enables any WAPS receiver that acquires theWAPS signal to provide accurate GPS time and frequency aiding tosignificantly reduce GNSS search requirements in a GNSS receiver.

In an embodiment of the system, the broadcast transmitters can beemployed ad hoc to provide localized indoor position determination. Forexample, in a fire-safety application, the WAPS transmitters would beplaced on three or more broadcast stations (could be fire trucks, forexample). The towers would synchronize to each other by one of the manymeans described earlier and broadcast signals. The bandwidth andchipping rates would be scaled based on spectrum availability andaccuracy requirements in that area for that application at that time.The receivers would be notified of the system parameters through thecommunication link to the devices.

FIG. 21 is a block diagram of a receiver unit, under an embodiment. Thebeacon signal is received at the antenna on the receiver unit,down-converted, demodulated and decrypted and fed to the positioningengine. The receiver provides all information to reconstruct the signalaccurately. The receive antenna can be an omni-directional antenna or,alternatively, a number of antennas/arrays providing diversity etc. Inanother embodiment, the mixing and down conversion can be done in thedigital domain. Each receiver unit includes or uses a unique hardwareidentification number and a computer generated private key. Eachreceiver unit, in general, stores the last few locations in non volatilememory and can be later queried remotely for the last few storedlocations. Based on the availability of the spectrum in a given area,the transmitters and receivers can adapt to the available bandwidth andchange the chipping rate and filter bandwidths for better accuracy andmultipath resolution.

In one embodiment, the digital baseband processing of the receivedsignals is accomplished using commercially-available GPS receivers bymultiplexing/feeding the signal from a GPS RF section with the WAPS RFmodule. FIG. 22 is a block diagram of the receiver with a WAPS RFmodule, under an embodiment. The RF module includes one or more of Lownoise amplifiers (LNAs), filters, down-converter, and analog to digitalconverters, to name a few. In addition to these components, the signalcan be further conditioned to fit the input requirements of the GPSreceiver using additional processing on chip or a custom ASIC or on anFPGA or on a DSP or on a microprocessor. The signal conditioning caninclude digital filtering for in-band or out-of band noise (such asACI—adjacent channel interference), translating intermediate or basebandfrequencies of the input to the GPS IC from the frequencies of the WAPSreceiver, adjusting the digital signal strength so that the GPS IC willbe able to process the WAPS signal, automatic gain control (AGC)algorithms to control the WAPS frontend etc. In particular, thefrequency translation is a very useful feature because this allows theWAPS RF module to work with any commercially available GPS receiver. Inanother embodiment, the entire RF frontend chain including the signalconditioning circuits for the WAPS system can be integrated onto anexisting GPS die that contains a GPS RF chain.

In another embodiment, if access to the digital baseband input is notavailable, the signal can be up-converted/down-converted from any bandto the GPS band and fed into the RF section of the GPS receiver. FIG. 23shows signal up-conversion and/or down-conversion, under an embodiment.

In another embodiment, multiple RF chains or tunable RF chains can beadded to both the transmitter and receiver of the WAPS system so as touse the most effective frequency of operation in a given area, be itwide or local. The choice of frequency can be determined by cleanlinessof the spectrum, propagation requirements, etc.

Similarly, WAPS can temporarily use a receive chain in a receiver systemthat includes multiple receive chains. For example, a wideband CDMA(W-CDMA) receiver system includes two receive chains to improve receivediversity. Thus, when WAPS is used in a W-CDMA receiver system one ofthe two native receive chains of the W-CDMA can be used temporarily forreceiving and processing WAPS signals. FIG. 24 is a block diagram of areceiver system having multiple receive chains in which one of thereceive chains can be used temporarily for receiving and processing WAPSsignals, under an embodiment. In this example, the diversity receivechain can be used to temporarily receive and process the WAPS signals.Alternatively, the GPS receive chain can be used to temporarily receiveand process the WAPS signals.

The radio front-end can be shared between WAPS and another application.Some parts of the frontend can be shared and some may be used on amutually exclusive basis. For example, if the die/system already has aTV (NTSC or ATSC or systems like DVB-H, MediaFLO) tuner front-endincluding the antenna, the TV tuner radio and antenna can be shared withthe WAPS system. They can operate on a mutually exclusive basis in that,either the system receives TV signals or receives WAPS signals at anygiven time. In another embodiment, if it makes it easier to add a WAPSRF section to such a system, the antenna can be shared between the TVtuner and the WAPS system allowing both systems to operatesimultaneously. In cases where the system/die has a radio like an FMradio, the RF front-end can be modified to accommodate both the WAPSsystem and the FM radio and these radios can operate on a mutuallyexclusive basis. Similar modifications can be done for systems that havesome RF frontends that operate in close frequency proximity to the WAPSRF band.

The clock source reference such as crystal, crystal oscillator (XO),Voltage Controlled Temperature Compensated Crystal Oscillator (VCTCXO),Digitally-controlled Crystal Oscillator (DCXO), Temperature CompensatedCrystal Oscillator (TCXO), that is used for a GNSS sub-system can beshared with the WAPS receiver to provide the reference clock to the WAPSreceiver. This sharing can be done on the die or off-chip.Alternatively, the TCXO/VCTCXO used by any other system on a cellularphone can shared with the WAPS system. FIG. 25 is a block diagramshowing clock sharing in a positioning system, under an embodiment. Notethat the transceiver or processor system block can refer to a variety ofsystems. The transceiver system that shares the clock with the WAPSsystem can be a modem transceiver (for example, a cellular or WLAN or BTmodem) or a receiver (for example, a GNSS, FM or DTV receiver). Thesetransceiver systems may optionally control the VCTCXO or DCXO forfrequency control. Note that the transceiver system and the WAPS systemmay be integrated into a single die or may be separate dies and does notimpact the clock sharing. The processor can be any CPU system (such asan ARM sub-system, Digital Signal Processor system) that uses a clocksource. In general, when a VCTCXO/DCXO is shared, the frequencycorrection applied by the other system may be slowed down as much aspossible to facilitate WAPS operation. Specifically, the frequencyupdates within the maximum integration times being used in WAPS receivermay be limited to permit better performance (i.e. minimizing SNR loss)for the WAPS receiver. Information regarding the state of the WAPSreceiver (specifically, the level of integration being used, acquisitionversus tracking state of the WAPS system) can be exchanged with theother system for better coordination of the frequency updates. Forexample, frequency updates could be suspended during WAPS acquisitionphase or frequency updates can be scheduled when the WAPS receiver is insleep state. The communication could be in the form of control signalsor alternatively in the form of messages exchanged between thetransceiver system and the WAPS system.

The WAPS broadcasts signals and messages from the towers in such a waythat a conventional GPS receiver's baseband hardware need not bemodified to support both a WAPS and a traditional GPS system. Thesignificance of this lies in the fact that although the WAPS system hasonly half the available bandwidth as the GPS C/A code system (whichaffects the chip rate), the WAPS broadcast signal is configured tooperate within the bounds of a commercial grade C/A code GPS receiver.Further, based on signal availability, the algorithms will decidewhether GPS signals should be used to determine position or WAPS signalsor a combination thereof should be used to get the most accuratelocation.

The data transmitted on top of the gold codes on the WAPS system can beused to send assistance information for GNSS in the cases of a hybridGNSS-WAPS usage scenario. The assistance can be in the form of SV orbitparameters (for example, ephemeris and almanac). The assistance may alsobe specialized to SVs visible in the local area.

In addition, the timing information obtained from the WAPS system can beused as fine time aiding for the GNSS system. Since the WAPS systemtiming is aligned to GPS (or GNSS) time, aligning to the code and bit ofWAPS signal and reading the data stream from any tower provides coarseknowledge of GNSS time. In addition, the position solution (thereceiver's clock bias is a by-product of the position solution)determines the WAPS system time accurately. Once the WAPS system time isknown, fine time aiding can be provided to the GNSS receiver. The timinginformation can be transferred using a single hardware signal pulsewhose edge is tied to the internal time base of WAPS. Note that the WAPSsystem time is directly mapped onto GPS time (more generally, with GNSStime, since the time bases of GNSS systems are directly related). TheGNSS should be able to latch its internal GNSS time base count uponreceipt of this edge. Alternatively, the GNSS system should be able togenerate a pulse whose edge is aligned to its internal time base and theWAPS system should be capable of latching its internal WAPS time base.The WAPS receiver then sends a message with this information to the GNSSreceiver allowing the GNSS receiver to map its time base to WAPS timebase.

Similarly, the frequency estimate for the local clock can be used toprovide frequency aiding to the GNSS receiver. Note that frequencyestimate from WAPS receiver can be used to refine the frequency estimateof the GNSS receiver whether or not they share a common clock. When thetwo receivers have a separate clock, an additional calibration hardwareor software block is required to measure the clock frequency of onesystem against the other. The hardware or software block can be in theWAPS Receiver section or in the GNSS receiver section. Then, thefrequency estimate from the WAPS receiver can be used to refine thefrequency estimate of the GNSS receiver.

The information that can be sent from the WAPS system to the GNSS systemcan also include an estimate of location. The estimate of location maybe approximate (for example, determined by the PN code of the WAPStower) or more accurate based on an actual position estimate in the WAPSsystem. Note that the location estimate available from the WAPS systemmay be combined with another estimate of position from a differentsystem (for example, a coarse position estimate from cellular ID basedpositioning) to provide a more accurate estimate of position that can beused to better aid the GNSS system. FIG. 26 is a block diagram ofassistance transfer from WAPS to GNSS receiver, under an embodiment.

The GNSS receiver can also help improve the performance of the WAPSreceiver in terms of Time-To-First-Fix (TTFF), sensitivity and locationquality by providing location, frequency and GNSS time estimates to theWAPS receiver. As an example, FIG. 27 is a block diagram showingtransfer of aiding information from the GNSS receiver to the WAPSreceiver, under an embodiment. Note that the GNSS system can be replacedby LORAN, e-LORAN or similar terrestrial positioning system as well. Thelocation estimate can be partial (eg. Altitude or 2-D position), orcomplete (eg. 3-D position) or raw range/pseudo-range data). Therange/pseudo-range data should be provided along with the location of SV(or means to compute the location of the SV such as SV orbit parameters)to enable usage of this range information in a hybrid solution. Alllocation aiding information should be provided along with a metricindicating its quality. When providing GNSS time information (which maybe transferred to the WAPS system using a hardware signal), the offsetof GNSS time relative to GPS time (if any) should be provided to enableusage in the WAPS receiver. Frequency estimates, can be provided as anestimate of the clock frequency along with a confidence metric(indicating the estimated quality of the estimate, for example, themaximum expected error in the estimate). This is sufficient when theGNSS and WAPS systems share the same clock source. When the GNSS andWAPS systems use a separate clock, the GNSS clock should also beprovided to the WAPS system to enable the WAPS system to calibrate (i.e.estimate the relative clock bias of WAPS with respect to GNSS clock) or,alternatively, the WAPS system should provide its clock to the GNSSsystem and the GNSS system should provide a calibration estimate (i.e.an estimate the relative clock bias of WAPS with respect to GNSS clock).

To further improve the sensitivity and TTFF of a WAPS receiver,assistance information (such as that would otherwise be decoded from theinformation transmitted by the towers) can be provided to the WAPSreceiver from a WAPS server by other communication media (such ascellular phone, WiFi, SMS etc). With the “almanac” information alreadyavailable, the WAPS receiver's job becomes simple since the receiverjust needs to time align to the transmit waveform (without requirementof bit alignment or decoding). The elimination of the need to decode thedata bits reduces TTFF and therefore saves power since the receiver doesnot need to be continuously powered on to decode all the bits. FIG. 28is an example configuration in which WAPS assistance information isprovided from a WAPS server, under an embodiment.

A beacon may be added to the receiver to further improve localpositioning. The beacon can include a low power RF transmitter thatperiodically transmits a waveform with a signature based on a device ID.For example, the signature can be a code that uniquely identifies thetransmitter. An associated receiver would be able to find a location ofthe transmitter with a relatively higher accuracy through either signalenergy peak finding as it scans in all directions, or through directionfinding (using signals from multiple-antenna elements to determinedirection of signal arrival).

Resolution of Multipath Signals

Resolution of multipath is critical in positioning systems. Wirelesschannel is often characterized by a set of randomly varying multipathcomponents with random phases and amplitudes. For positioning to beaccurate, it is imperative that the receiver algorithm resolves theline-of-sight (LOS) path if present (it will be the first arriving path)or the path that arrives first (which may not necessarily be the LOScomponent).

Traditional methods often work as follows: (1) the received signal iscross-correlated with the transmitted pseudo-random sequence (e.g. Goldcode sequence, which is known at the receiver); (2) the receiver locatesthe first peak of the resulting cross-correlation function and estimatesthat the timing of the path that arrived first is the same as the timingindicated by the position of this peak. These methods work effectivelyas long as the lowest multipath separation is much larger than inverseof the bandwidth available which is often not the case. Bandwidth is aprecious commodity and a method which can resolve multipath with theminimal amount of bandwidth is highly desired to improve the efficiencyof the system.

Depending on the channel environment (including multipath and signalstrength), an appropriate method for obtaining an estimate of theearliest arriving path is used. For best resolvability, high-resolutionmethods are used whereas for reasonable performance at low SNRs moretraditional methods that directly use the cross-correlation peak samplesand some properties of the correlation function around the peak areapplied.

Consider the quantized received signal y[n] sampled at a rate f_(s)given by:

y[n] = h_(eff)[n] ⊗ x[n]${y\lbrack n\rbrack} = {\sum\limits_{i = n_{0}}^{\infty}\;{{h_{eff}\lbrack i\rbrack} \cdot {x\left\lbrack {n - i} \right\rbrack}}}$where y[n] is the received signal which is the convolution of thetransmitted pseudo-random sequence x[n] with the effective channelh_(eff)[n]=h[n]⊗h_(tx)[n]⊗h_(rx)[n], where h_(tx)[n] is the transmitfilter, h_(tx)[n] is the receive filter and h[n] is the multi-pathchannel.

One method to find the peak position is by peak interpolation using thevalues surrounding the apparent peak position. The interpolation may bequadratic using one value on either side of the peak or may use a higherorder polynomial using two or more samples around the peak or may use abest fit for the actual pulse shape. In the case of quadraticinterpolation, a quadratic is fitted to the peak value and the valuesimmediately surrounding the peak. The peak of the quadratic determinesthe peak position that is used for ranging. This method is quite robustand can work well at low SNR.

An alternative embodiment may use a value other than the peak positionas the reference position. Note that the DLL actually uses the peakposition as reference position on the correlation function whereas thismethod uses a point different from the peak as reference. This method ismotivated by the fact that the early edge of the correlation peak isless affected by multi-path than the trailing edge. For example, a point75% of chip T_(c) from the peak on the undistorted (without channeleffects) correlation function may be used as a reference point. In thiscase, the portion of the interpolated z[n] function that matches this75% point is selected and the peak is found as 25% of T_(c) away fromthis point.

Another alternative peak correlation function based method may use thepeak shape (such as a measure of distortion of the peak, for example,peak width). Starting from the peak location and based on the shape ofthe peak, a correction to the peak location is determined to estimatethe earliest arriving path.

High-resolution methods are a class of efficient multipath-resolutionmethods which use Eigen-space decompositions to locate the multipathcomponents. Methods such as MUSIC, ESPRIT fall under this class ofresolution schemes. They are highly powerful schemes as in they canresolve effectively much more closely spaced multipath components thantraditional methods, for the same given bandwidth. The high resolutionearliest time of arrival method attempts to estimate directly the timeof arrival of earliest path rather than inferring the peak position fromthe peak values. The below assumes that a coarse-acquisition of thetransmitted signal is already available at the receiver and the start ofthe pseudo-random sequence is known roughly at the receiver.

FIG. 29 is a flow diagram for estimating an earliest arriving path inh[n], under an embodiment. The method to determine the earliest pathcomprises the following operations, but is not so limited:

-   -   1. Cross-correlate the received samples y[n] with the transmit        sequence x[n] to obtain the result z[n]. When the        cross-correlation is written in terms of a convolution,        z[n]=y[n]⊗x*[−n]        -   The equation can be re-written as            z[n]=h _(eff)[n]⊗ϕ_(xx)[n]            where ϕ_(xx)[n] is the autocorrelation function of the            pseudo-random sequence    -   2. Locate the first peak of z[n] and denote it as n_(peak).        Extract wL samples to the left of the peak and wR samples to the        right of the peak of z[n] and denote this vector as pV.        pV=[z[n _(peak) −wL+1] . . . z[n _(peak) +wR]]        The vector pV denotes the useful part of the cross-correlation        result z[n]. In the ideal case, in the absence of channel        distortion and when the channel BW is not limited, the choosing        wL=wR=ƒ_(s)T_(c) would be sufficient to determine the timing of        the received signal. In the presence of limited BW, for the case        when the pseudo-random code x[n] is a sequence of +1/−1's, the        optimal method to choose wL and wR are to choose them as the        non-zero values (or, more generally, values> a certain threshold        defined as a fraction of the peak value are selected) present on        the left and right side of the peak of p[n]=h_(tx)[n]⊗h_(tx)[n]        respectively. One other consideration in the choice of wL and wR        is to select enough uncorrelated noise samples to obtain enough        information regarding the noise sub-space. In addition, the        integers wL and wR should be chosen to include all possible        multipath components especially on the left side (i.e. through        choice of wL) to help resolve far-out multipath components.        Including too many samples beyond ƒ_(s)T_(c) increases the        amount of noise introduced in the pV vector and hence has to be        curtailed. Through simulation and experiments, a typical set of        values for wL and wR are 3ƒ_(s)T_(c) and 3ƒ_(s)T_(c),        respectively. Note that z[n] (and in turn pV) contains the        effect of the channel h[n], the transmit filter h_(tx)[n], the        receive filter h_(rx)[n] and the autocorrelation function of the        pseudo-random sequence ϕ_(xx)[n]. In order to estimate the        earliest arriving path in the channel, the other effects need to        be eliminated. In many cases the transmit and receive        pulse-shapes are matched for best noise performance, but that        constraint is not required for this algorithm to work. The        reference correlation function is defined as        ϕ_(ref)[n]=ϕ_(xx)[n]⊗h_(tx)[n]⊗h_(rx)[n] which needs to be        estimated and eliminated before pV can be used for estimation of        earliest arriving path.    -   3. The Reference correlation function ϕ_(ref)[n] is estimated        next.        -   One method to obtain the reference cross-correlation is as            follows: perform steps 1-2 on a ideal channel (a so called            “cabled link”) to obtain the corresponding peak vector            pV_(Ref). The peak vector pV_(Ref) contains the useful            samples of the reference correlation function ϕ_(ref)[n].            FIG. 30 is a flow diagram for estimating reference            correlation function, under an embodiment.        -   The “Cabled link” method involves sending the modulated            signal from the transmitter front-end (power-amplifier and            transmit antenna is by-passed) through an ‘ideal’ channel            (for example, a cable) to the receiver front-end (bypass the            receive antenna). Note that the ‘ideal’ channel can have            some delay and attenuation, but should not add any other            distortion and must have high SNR. For the best performance,            the ‘cabled’ reference needs to be generated separately for            each pseudo-random sequence as they have different            autocorrelation functions and hence different references. It            is also then critical to choose PRNs properly for the best            autocorrelation functions (specifically, their close in            autocorrelation side-lobes should be well suppressed            compared to the peak) which will result in the best overall            performance of the timing-resolution method, since            autocorrelation sidelobes can get mistaken for multipath            unless sufficiently attenuated.        -   Assuming transmit filter responses are controlled, one            calibration of the response on cabled link is required per            receiver during production. If receiver filter            characteristics can be controlled (for example, for a bunch            of receivers), then the calibration on cabled link of the            response can be further reduced to one calibration            measurement for a set of receivers.        -   An alternative method for determining the reference            correlation function ϕ_(ref)[n] is to compute the individual            components ϕ_(xx)[n], h_(tx)[n] and h_(rx) [n] analytically            and to convolve them to arrive at the reference correlation            function ϕ_(ref)[n]. Note that this method depends on the            extent to which transmit and receive filter impulse            responses can be controlled in an actual implementation.    -   4. Improve the SNR in the estimate of pV by coherently averaging        across multiple gold codes and even across multiple bits.        Averaging across multiple bits can be done coherently after        decisions on the individual bits being transmitted have been        made. In other words using decision feedback before integration        across bits. Note that improved SNR can be obtained equivalently        by performing averaging in the cross-correlation function        estimation in Step 1.    -   5. Calculate the Fast Fourier Transform (FFT) of length N_(fft)        of pV and pV_(Ref) with zero padding of N_(fft)−(wL+wR) zeros to        obtain the length N_(fft) vectors pV_(Freq) and pV_(Ref,Freq)        respectively. An optimal value for N_(fft) is obtained by        checking resolvability of multipath through simulations using        both synthetic and real measured channels. A typical value of        N_(fft) was found to be greater than or equal to 4096. The        pV _(Freq)=FFT[pV zeropad]        pV _(Ref,Freq)=FFT[pV _(Ref) zeropad]    -   6. Calculate

${H_{full}\lbrack k\rbrack} = \frac{{pV}_{Freq}\lbrack k\rbrack}{{pV}_{{Ref},{Freq}}\lbrack k\rbrack}$to obtain the frequency domain estimate (corrupted with noise) of thechannel h[n]. If the received sequence y[n] is oversampled by N_(os)(i.e.

$N_{os} = \frac{f_{s}T_{c}}{2}$for a transmit pulse shape band-limited to +/−1/Tc) and if the transmitand receive pulse-shaping filters are perfectly band-limited withBW=1/Tc, then exactly

$N = \frac{N_{fft}}{2N_{os}}$positive and negative samples around DC of H_(full)[k] are non-zero(i.e. usable) for estimation of the real channel, H_(real)[k]. From ourstudies, we have concluded that

$\frac{N_{fft}}{2\alpha\; N_{os}}$samples on either side of DC should be picked for the best performanceof the resolution algorithm, where α>1 is chosen based on the actualpulse-shaping filters used at the transmitter and receiver and theautocorrelation function ϕ_(xx)[n]. Note that including the frequencytransition band of ϕ_(ref)[n] causes noise enhancement and α is chosenlarge enough to exclude these frequencies in the selected samples.However, choosing α too large will cause loss of signal information. Apreferred choice of α=1.25 for real band-limited functions based onraised-cosine filter shapes with small excess bandwidth has been used inthe implementation.

-   -   7. If the DC component of H_(full)[k] is at index 0, the reduced        H vector, H[ ] is defined as:        H=[H _(full)[N _(fft) −N+1] . . . H _(full)[N _(fft)]H        _(full)[0]H _(full)[1] . . . H _(full)[N]]    -   8. Construct the matrix P from the reduced channel estimate        vector H[k],

$P = \left\lbrack \begin{matrix}{H(M)} & \ldots & {H\left( {{2\; N} - 1} \right)} \\{H\left( {M - 1} \right)} & \ldots & {H\left( {{2\; N} - 2} \right)} \\\vdots & \ddots & \vdots \\{H(0)} & \ldots & {H\left( {{2\; N} - M + 1} \right)}\end{matrix} \middle| \begin{matrix}{H^{\prime}(0)} & \ldots & {H^{\prime}\left( {{2\; N} - M + 1} \right)} \\{H^{\prime}(1)} & \ldots & {H^{\prime}\left( {{2\; N} - M + 2} \right)} \\\vdots & \ddots & \vdots \\{H^{\prime}(M)} & \ldots & {H^{\prime}\left( {{2\; N} - 1} \right)}\end{matrix} \right\rbrack$where 1<M<2N is a parameter and ( )′ represents conjugate of the complexnumber. Define the estimated covariance matrix R of the reduced channelestimate vector H[k] asR=P×P′If M is chosen to be too small (close to 1), then the eigen-values of Rare very limited in number and, as a result, the high-resolutionalgorithm cannot delineate between the signal and noise. If M is chosentoo large (close to 2N), then the covariance matrix estimate R isunreliable as the amount of averaging in obtaining the covariance isinadequate and also the covariance matrix R obtained is rank-deficient.Thus, a value of M which is right in the middle of its allowable rangei.e. M=N is a good choice. This has also been verified empirically.

-   -   9. Perform singular value decomposition (SVD) on R as        R=UDV′        Where U is a matrix of the left singular vectors, V is the        matrix of the right singular vectors and D is the diagonal        matrix of singular values.    -   10. Construct the vector of sorted singular values sV as        -   sV=diagonal elements of D sorted in descending order    -   11. The next key step is to separate the signal and noise        subspaces. In other words, to select an index ns in the vector        sV such that the singular values sV[ns+1] . . . sV[N] correspond        to noise. Define a vector of noise singular values as        sV_(noise).        -   There are a number of methods possible to separate the            singular values corresponding to the noise subspace and find            a representation for the basis vectors of the noise            sup-space:        -   a) All singular values which are smaller than

$\frac{\max({sV})}{T_{1}}$where T₁ is a threshold value which is a function of the signal-noiseratio (e.g. SNR on the chip) T₁=ƒ (SNR).

-   -   -   -   FIG. 31 is a flow diagram for estimating noise                sub-space, under an embodiment.

        -   b) All singular values less than min

${\min\left( {\frac{\max({sV})}{T_{1}},{{{mean}\left( {{sV}\left( {L\text{:}M} \right)} \right)} \times T_{2}}} \right)},$where L is a parameter which can be chosen greater than delay-spread(e.g. N/2) and T₂ is another threshold value determined empirically(typical value can be 1000).

-   -   -   -   FIG. 32 is a flow diagram for estimating noise                sub-space, under an alternative embodiment.

        -   c) Another method involves determining the noise subspace by            repeatedly estimating the SNR for different partitions of            noise and signal-plus-noise subspaces and comparing with            another estimate of SNR. FIG. 33 is a flow diagram for            estimating noise sub-space, under another alternative            embodiment.            -   1) Calculate estimate of SNR as follows:                -   i. Assume that the noise is represented by the sV( )                    n_(s),n_(s)+1 . . . M, Calculate noise variance as:

${\sigma_{est}^{2}\left( n_{s} \right)} = \frac{\sum\limits_{i = n_{s}}^{M}{{sV}(i)}}{M - n_{s} + 1}$

-   -   -   -   -   ii. Calculate the signal power as                    P_(sig)(n_(s))=τ_(i=1) ^(n) ^(s) ⁻¹(sV(i)−σ_(est)                    ²(n_(s)))                -   iii. Estimate of SNR:

${{SNR}_{est}\left( n_{s} \right)} = \frac{P_{sig}\left( n_{s} \right)}{\sigma_{est}^{2}\left( n_{s} \right)}$

-   -   -   -   2) An alternative estimate of SNR is obtained through                other methods (e.g. SNR on chip). One method of                estimating SNR directly is as follows:                -   i. If the received data samples (after frequency                    error removal and re-sampling to Tc-spaced samples                    and code de-correlation) are given by X_(i) (where                    the X_(i) are chip-spaced starting from the                    interpolated peak position).                    X _(i) =S+N _(i)                -   ii. The signal is estimated as

$\hat{S} = {\frac{1}{N}{\sum\limits_{i = 0}^{N - 1}X_{i}}}$

-   -   -   -   -   iii. The noise is estimated as

$\hat{N} = {\frac{1}{N - 1}{\sum\limits_{i = 0}^{N - 1}\left( {X_{i} - \hat{S}} \right)^{2}}}$

-   -   -   -   -   iv. The SNR is estimated as

$= \frac{\hat{S}}{\hat{N}}$

-   -   -   -   3) Choose the noise singular values as sV(ns, ns+1, . .                . , M) which satisfy the following condition:                n _(start)=[smallest n _(s) :SNR _(est)(n _(s))>                ]

        -   d) Another method involves determining the noise subspace by            repeatedly estimating the SNR for different partitions of            noise and signal subspaces using c)1) and choosing a            partition n_(start) such that n_(start)=argmax_(n) _(s)            [SNR_(est)(n_(s))−SNR_(est)(n_(s)−1)]_(n) _(s) ₌₂ ^(K).            -   FIG. 34 is a flow diagram for estimating noise                sub-space, under yet another alternative embodiment.

        -   e) FIG. 35 is a flow diagram for estimating noise sub-space,            under still another alternative embodiment.            -   1) Define

${wLen} = {\frac{{wL} + {wR}}{f_{s}T_{c}}.}$Then the first wLen singular values represent the significantsignal-plus-noise subspace or noise subspace singular values (the restof the singular values represent correlated noise and signal andquantization effects).

-   -   -   -   2) Calculate estimate of SNR as follows:                -   i. Assume that the noise is represented by the                    sV(i):i=n_(s), n_(s)+1 . . . wLen; 1<n_(s)≤wLen,                    calculate noise variance as:

${\sigma_{est}^{2}\left( n_{s} \right)} = \frac{\sum\limits_{i = n_{s}}^{wLen}{{sV}(i)}}{{wLen} - n_{s} + 1}$

-   -   -   -   -   ii. Calculate the signal power as                    P_(sig)(n_(s))=Σ_(i=1) ^(n) ^(s) ⁻¹[sV(i)−σ_(est)                    ²(n_(s))]                -   iii. Estimate of SNR:

${{SNR}_{est}\left( n_{s} \right)} = \frac{P_{sig}\left( n_{s} \right)}{\sigma_{est}^{2}\left( n_{s} \right)}$

-   -   -   -   3) Define n_(start)=[smallest                n_(s):SNR_(est)(n_(s))>(SNR_(est)(wLen)−thresDB)]. Then                n_(start) up to winLen represent the noise singular                values. A typical value of thresDB is 10.

    -   12. Choose the corresponding noise right-singular vectors to        build V_(N) i.e. choose all vectors in V which correspond to the        noise singular values and build the noise subspace matrix V_(N).

    -   13. Estimate Time of Arrival of the first path:        -   a) Define

${\omega(\tau)} = \begin{bmatrix}1 & e^{\frac{j\; 2\;\pi}{N_{fft}}\tau} & e^{\frac{j\; 2\;\pi}{N_{fft}}2\tau} & e^{\frac{j\; 2\;\pi}{N_{fft}}3\tau} & \ldots & e^{\frac{j\; 2\;\pi}{N_{fft}}{({M - 1})}\tau}\end{bmatrix}^{H}$

-   -   -   b) Calculate

${\Omega(\tau)} = \frac{1}{{\omega(\tau)}^{H}V_{N}V_{N}^{H}{\omega(\tau)}}$for a range of values of τ(τ∈[τ_(max), −τ_(max)]). The resolution ofsearch Δτ can be chosen as small as required. As an example, τ_(max)=5and ΔT=0.05 so that τ is searched for in the range [−5, 5] in steps of0.05.

-   -   14. Peaks of Ω(τ) will provide the positions of channel impulses        relative to the coarse peak, n_(peak). Theoretically, first peak        will correspond to LOS path. Based on information about the        propagation environment which could be encoded in the        transmission from the base-station, it is possible to control        τ_(max). For example, if the delay-spread is large, then τ_(max)        can be chosen to be larger (e.g. 10) and if it is less then        τ_(max) can be chosen as a smaller value (e.g. 4).        Combination Methods:        Apart from the standalone methods discussed above, numerous        other combination methods are possible. Combination of schemes        based on SNR on chip is an effective method. The following        describes a list of combination schemes that can be realized in        practice:    -   1. For chipSNR less than chipSNRRef, pick method 12(d) to choose        noise singular values. Otherwise choose method 12(a).    -   2. For chipSNR greater than chipSNRRef, pick method 12(d) to        choose noise singular values and estimate peak position.        Otherwise, use direct peak estimation techniques (such as peak        interpolation, peak shape) starting from the cross-correlation        function z[n].    -   3. For chipSNR less than chipSNRRef, pick method 12(e) to choose        noise singular values. Otherwise choose method 12(a).        -   A typical value of chipSNRRef is 10 dB.            Computation of Position

The location of the receiver unit is determined by the positioningengine available either on the terminal unit or the server. The receivercan use the range measurements from the system or combine the systemrange measurements with any of the measurements from other signals ofopportunity. A sufficient set of range measurements yields a positionfix provided that the measurements derive from known locations. Therange equation in 3D space is given byr _(i)=√{square root over ((x _(i) −X)²+(y _(i) −Y)²+(z _(i) −Z)²)}.

The location of the transmitters is given by (x_(i), y_(i), z_(i)) andthe unknown location of the mobile units is given by (X, Y, Z) in somelocal coordinate frame. Three or more transmitters produce three or morerange measurements that are used to compute a fix. The measurement has areceiver time bias additive term as well, because the receiver time isnot synchronized to the WAPS timing.R _(i) =r _(i) +cΔt.This equation is referred to later as “Pseudorange MeasurementEquation”. Note that the time bias is common because the transmittersare timing synchronized. The pseudoranges must be corrected for transmittiming corrections which are available from the data stream embedded inthe transmission from each transmitter. This delta time bias creates anew unknown parameter, so a minimum of four measurements are used for asolution. A barometric altimeter measurement provides the neededinformation for a solution asBaro=(z _(b) −Z).

One method of solving these non-linear simultaneous equations is tolinearize the problem at an arbitrary initial point and then iterativelyfinding corrections to this initial position to iteratively leads to thefinal solution.

This method uses an initial guess for the X, Y, Z solution, so thecentroid of the transmitters is used as

$\left( {X_{0},Y_{0},Z_{0}} \right) = {\left( {1/n} \right){\sum\limits_{i = 1}^{n}{\left( {x_{i},y_{i},z_{i}} \right).}}}$The final position solution is assumed to be of the form(X,Y,Z,Δt)=(X ₀ ,Y ₀ ,Z ₀ ,Δt ₀=0)+(dX,dY,dZ,dΔt)The geometric range can be expanded in a Taylor series about(X,Y,Z,Δt)=(X₀,Y₀,Z₀, Δt₀)

$\begin{matrix}{R_{i} = {\sqrt{\left( {x_{i} - X} \right)^{2} + \left( {y_{i} - Y} \right)^{2} + \left( {z_{i} - Z} \right)^{2}} + {c\;\Delta\; t}}} \\{= {\sqrt{\left( {x_{i} - X_{0}} \right)^{2} + \left( {y_{i} - Y_{0}} \right)^{2} + \left( {z_{i} - Z_{0}} \right)^{2}} + {c\;\Delta\; t_{0}} +}} \\{\left. \frac{\partial r}{\partial x} \middle| {}_{({X_{0},Y_{0},Z_{0},{\Delta\; t_{0}}})}{{dX} + \frac{\partial r}{\partial y}} \middle| {}_{({X_{0},Y_{0},Z_{0},{\Delta\; t_{0}}})}{{dY} +} \right.} \\{\left. \frac{\partial r}{\partial z} \middle| {}_{({X_{0},Y_{0},Z_{0},{\Delta\; t_{0}}})}{{dZ} + {{cd}\;\Delta\; t}} \right.} \\{= \left. {{\hat{r}}_{i} + \frac{\partial r}{\partial x}} \middle| {}_{({X_{0},Y_{0},Z_{0},{\Delta\; t_{0}}})}{{dX} + \frac{\partial r}{\partial y}} \middle| {}_{({X_{0},Y_{0},Z_{0},{\Delta\; t_{0}}})}{{dY} +} \right.} \\{\left. \frac{\partial r}{\partial z} \middle| {}_{({X_{0},Y_{0},Z_{0},{\Delta\; t_{0}}})}{{dZ} + {{cd}\;\Delta\; t}} \right.}\end{matrix}$where the estimated ranges are computed as{circumflex over (r)} _(i)=√{square root over ((x _(i) −X ₀)²+(y _(i) −Y₀)²+(z _(i) −Z ₀)²)}.and the partial derivatives are given by∂R/∂x=∂r/∂x=(x _(i) −X)/r _(i) ∂R/∂Δt=c∂R/∂y=∂r/∂y=(y _(i) −Y)/r _(i)∂R/∂z=∂r/∂z=(z _(i) −Z)/r _(d).

In this embodiment, four linear equations with four unknowns are shown.Additional range estimates would produce more rows in the matrix. Theresult is the set of equations

${\begin{bmatrix}{\left( {x_{1} - X_{0}} \right)/{\hat{r}}_{1}} & {\left( {y_{1} - X_{0}} \right)/{\hat{r}}_{1}} & {\left( {z_{1} - Z_{0}} \right)/{\hat{r}}_{1}} & 1 \\{\left( {x_{2} - X_{0}} \right)/{\hat{r}}_{2}} & {\left( {y_{2} - Y_{0}} \right)/{\hat{r}}_{2}} & {\left( {z_{2} - Z_{0}} \right)/{\hat{r}}_{1}} & 1 \\{\left( {x_{3} - X_{0}} \right)/{\hat{r}}_{3}} & {\left( {y_{3} - Y_{0}} \right)/{\hat{r}}_{3}} & {\left( {z_{3} - Z_{0}} \right)/{\hat{r}}_{1}} & 1 \\0 & 0 & 1 & 0\end{bmatrix} \times \begin{bmatrix}{\delta\; X} \\{\delta\; Y} \\{\delta\; Z} \\{c\;\delta\;\Delta\; t}\end{bmatrix}} = \begin{bmatrix}{R_{1} - {\hat{r}}_{1}} \\{R_{2} - {\hat{r}}_{2}} \\{R_{3} - {\hat{r}}_{3}} \\{z_{b} - Z_{0}}\end{bmatrix}$The last row of the observation matrix represents the barometricaltimeter measurement. The column of three 1 represents the same timebias on all three ranges. These equation are in the form of Ax=b. Thesolution x=A⁻¹*b. Note that in the absence of a barometer measurement,one more additional measurement would add an additional row similar torows 1 to 3 of the matrix above. This additional measurement wouldenable estimation of the altitude of the receiver. Note that when thereare more measurements available than the number of unknowns, then thesolution would be based on the pseudoinverse of A given byA₊=(A^(T)A)⁻¹A^(T) and the least square solution is given by x=A₊ ⁻¹b.When the quality of measurements are not equal, the optimal way ofsolving the equations Ax=b in the least square sense is to use a weightproportional to the SNR for the error from each equation. This leads toa solution x=A₊ ⁻¹b with A₊=(A^(T) WA)⁻¹A^(T)W. The diagonal weightingmatrix W formed by the weight proportional to the noise variance of themeasurements. The solution of these equations produces a deltacorrection to the X, Y, Z and delta time estimates, such that

$\begin{bmatrix}X_{1} \\Y_{1} \\Z_{1} \\{\Delta\; t_{1}}\end{bmatrix} = {\begin{bmatrix}X_{0} \\Y_{0} \\Z_{0} \\{\Delta\; t_{0}}\end{bmatrix} + {\begin{bmatrix}{\delta\; X} \\{\delta\; Y} \\{\delta\; Z} \\{\delta\;\Delta\; t}\end{bmatrix}.}}$

This completes the first iteration of the method. The updated positionand time bias estimates replace initial guess and the algorithm continueuntil the delta parameters are below some threshold value. A typicalstopping point would be for the norm of the delta values are below acertain threshold (for example, one meter).

The system of linearized equations in the GPS is solved using leastsquares and an initial guess about the location of the user such thatthe algorithm converges to the final user location. The linearization isbased on the fundamental assumption that the distance between thesatellites and the user position is larger than the distance between theuser position on the earth and the guessed position. For the same set ofequations to work in a terrestrial environment (with small geometry),the initial guess can be based on the centroid (as above), a point closeto the transmitter from which the received signal is the strongest, orobtained by a direct method which gives a closed form solution by meansof a sequence of formulae with no iterations. When the initial guess isa centroid or a point close to the transmitter from which the receivedsignal is the strongest, the initial guess is improved using a leastsquares method. When the initial guess is obtained by a direct methodwhich gives a closed form solution by means of a sequence of formulaewith no iterations, the initial solution itself is the final solutionand it is improved using least squares only when there are moremeasurements (and hence equations) than unknowns with individualmeasurements weighted by using the expected errors in those measurements(which are obtained from such parameters as signal strength andelevation angle). Further, if a sequence of measurements is to beprocessed in time, a solution obtained as above may be fed to a Kalmanfilter to obtain an optimal solution “trajectory”.

Another approach that overcomes the linearization problem in terrestrialcases involves formulating the set of equations as a non-linearminimization problem (specifically as a weighted non-linear leastsquares problem). Specifically, the non-linear objective function to beminimized is defined as

${f\left( {X,Y,Z,{\Delta\; t}} \right)} = {\sum\limits_{i = 0}^{N - 1}{W_{i} \times \left\lbrack {R_{i} - \sqrt{\left( {x_{i} - X} \right)^{2} + \left( {y_{i} - Y} \right)^{2} + \left( {z_{i} - Z} \right)^{2}} - {\Delta\; t}} \right\rbrack^{2}}}$The weights W_(i) are chosen to be inversely proportional to the SNR ofthe measured ranges R_(i). The best estimate of the receiver location isobtained as the set of (X,Y,Z,Δt) that minimizes the objective function.When barometer or other altitude aiding is available then the objectivefunction gets modified to

${f\left( {X,Y,{Z = Z_{baro}},{\Delta\; t}} \right)} = {\sum\limits_{i = 0}^{N - 1}{W_{i} \times \left\lbrack {R_{i} - \sqrt{\left( {x_{i} - X} \right)^{2} + \left( {y_{i} - Y} \right)^{2} + \left( {z_{i} - Z_{baro}} \right)^{2}} - {\Delta\; t}} \right\rbrack^{2}}}$

The position solution based on this method will be more stable androbust, particularly under small geometry terrestrial systemconfiguration. In this configuration, small changes in receivercoordinates significantly changes the observation matrix and sometimesleads to lack of convergence of the linearized iterations. Convergenceto a local minimum or divergence occurs more often due to residual biasin the measurements which affects the shape of the objective function sothat local minima can be present. Residual bias can be quite common inindoor/urban canyon environments. The non-linear formulation above makesthe position algorithm robust to measurement bias besides overcoming thesmall geometry linearization problem.

One approach to perform the minimization of the function ƒ to obtainoptimal X, Y, Z is to use a genetic algorithm (such as differentialevolution) to find the global minimum of the function. The use of suchan algorithm enables the solution to avoid local minima that occur insmall geometry terrestrial positioning when multi-path bias is presentin the range measurements.

Irrespective of whether linearized least squares or non-linear leastsquares method is used to solve the pseudo-range measurement equations,it is important for a quality metric to be provided along with aposition estimate. The position quality metric should be a function ofthe pseudo-range measurement equation residuals, the quality of themeasurements as well as the geometry of the towers relative to theestimated position. The pseudo-range measurement residual for the ithtower measurement is given byPR _(res,i) =R _(i)−(√{square root over ((x _(i) −X)²+(y _(i) −Y)²+(z_(i) −Z)²)}+cΔt)The average weighted rms pseudo-range residual is given by

${PR}_{res} = \sqrt{\left( \frac{\sum\limits_{i}{W_{i} \times {PR}_{{res},i}^{2}}}{\sum\limits_{i}W_{i}} \right)}$The HDOP, VDOP, PDOP are defined from the diagonal elements of H=(A^(T)A)⁻¹A^(T) asHDOP=√{square root over (H(1,1)+H(2,2))}VDOP=H(3,3)PDOP=√{square root over (H(1,1)+H(2,2)+H(3,3))}The pseudo-range RMS (root-mean-square) error at a particular SNR isgiven byPRE _(th)=ƒ(√{square root over (SNR)})where ƒ is generally a non-linear monotonic decreasing function of itsargument. The function ƒ can be derived analytically for a particularreceiver configuration as a function of signal BW and receiver BW oralternatively, found from simulation as a table mapping SNR to rangeerror.

The quality metric for 2-D position is defined asQM _(2-D) =HDOP×√{square root over (PR _(res) ² +PRE _(th) ²)}×αSimilarly, the quality metric for the altitude and 3-D position is givenbyQM _(alt) =VDOP×√{square root over (PR _(res) ² +PRE _(th) ²)}×αQM _(3-D) =PDOP×√{square root over (PR _(res) ² +PRE _(th) ²)}×αThe quantity α is chosen based on the level of confidence desired. Forexample, a value of 3 would be used to obtain 95% confidence, while avalue of 1 would be used for 68% confidence.

Another method of positioning using the WAPS system involves the use ofa WAPS reference receiver in a differential scheme. As shown in“Differential Wide Area Positioning System” and discussed in the contextof timing synchronization, the time-stamped reference receivermeasurements along with the latitude, longitude, altitude of the WAPStowers and the reference receiver can be used to determine the timingdelta between WAPS tower transmissions at the specific time-stamp. Oncethe timing delta between transmitters is known, the range equations canbe reduced to have a single common time bias again. The WAPS receiverthen can avoid demodulation of the WAPS data stream (for example, toextract the timing corrections from the data stream). The WAPS receivermeasurements can be sent to the server and the position can then becomputed at the server or, alternatively, the reference receivermeasurements can be relayed to the WAPS receiver and the position can becomputed there. It is assumed that the latitude, longitude and altitudeof the WAPS towers is already known/available for use in the positioncomputation. In the case that the WAPS data stream is secure, thisdifferential system can avoid the need to extract data from the securedata stream for timing correction purposes.

Another alternative method for obtaining positioning from the WAPSsystem uses RSSI finger-printing techniques. A database of WAPS towertransmit powers/locations and RSSI levels is built up for a given targetarea based on training measurements in the area for which positioning isrequired. Note that RSSI database can also be augmented with Angle ofArrival (AOA) information to improve the solution. The WAPS receiverRSSI measurements (and possibly AOA measurements) are then used to lookup this database to obtain a location estimate. An alternative method ofusing the WAPS RSSI measurements would be to translate the measurementsinto a range estimate using a propagation model (or simpleextrapolation/interpolation techniques) and then use tri-lateration todetermine the position. Note that the RSSI measurements in thesefinger-printing techniques can be replaced by any other measurementsthat can be translated to range.

An alternative method of computing position using the WAPSinfrastructure uses a blind method for obtaining positioning from theWAPS system without prior knowledge of the WAPS tower locations. In thismethod, the approximate location of the WAPS towers are determined byfield measurement (for example, by measuring RSSI from many anglesaround the WAPS tower at GNSS tagged locations and then using a weightedaverage based on RSSI of these locations to estimate WAPS towerlocations). Then, any of the RSSI finger-printing methods can be used todetermine position (for example, as described in the above paragraph).

An alternative method of computing position using the WAPSinfrastructure can be used for computing position offline. The positioncomputation involves storing the sample segments of the WAPS signal (forexample, the stored data may be I data at low IF or IQ data at baseband)from the WAPS receiver along with optionally an approximate position anda WAPS time tag. Note that it is enough to store enough samples to beable to acquire the signal. The samples are processed at a later time tosearch, acquire and compute range to WAPS towers. The method may useoffline data to look-up tower locations and timing correctioninformation that may be stored in a central database on a server. Thismethod of offline position computation provides the ability to supportWAPS positioning at the cost of only memory on the device. The otheradvantage of this method is the time taken for storing the WAPS IQ datais very short, making it convenient for applications that need to tagposition quickly, but the exact position is not requiredinstantaneously. One possible application for this method can be forgeo-tagging of photographs.

Another approach to positioning uses carrier phase measurements inaddition to the code phase measurements indicated above. The carrierphase measurements can be written as:ϕ_(i)(t ₀)=r _(i)(t ₀)+N _(i) λ+ΔtVarious techniques can be used to resolve the integer ambiguity N_(i) inthe carrier phase measurements. Code phase measurements, measurements atmultiple frequencies and/or other methods can be used to resolve theambiguities. Subsequently, the carrier phase measurements at time t_(k)can provide accurate tracking of position starting from an accurateinitial position. The carrier phase measurements at future times can bewritten asϕ_(i)(t _(k))=r _(i)(t _(k))+N _(i) Δ+Δt

The N_(i) do not change as long as the carrier phase measurements do nothave cycle slips (i.e. the signals should be tracked with continuousphase lock) and the new locations can be computed using least squares.Alternatively, these measurements can be used in a Kalman filter toupdate the new position state. If phase lock is lost, new values ofinteger ambiguity need to calculated.

Another approach uses differential positioning relative to a referencereceiver as described above. Differential positioning can be done usingeither code or carrier measurements or a combination of both. Singledifference observables are computed for code and carrier phase bysubtracting measurements of the same towers from reference receiver rand receiver s as

$R_{sr}^{i} = {\underset{\underset{{{geometrical}\mspace{14mu}{range}}{difference}}{︸}}{\rho_{s}^{i} - \rho_{r}^{i}} + \underset{\underset{{{time}\mspace{14mu}{difference}}{{between}\mspace{14mu}{clocks}}}{︸}}{c\left( {{dt}_{s} - {dt}_{r}} \right)} + \left( {ɛ_{R,s} - ɛ_{R,r}} \right)}$$\Phi_{sr}^{i} = {\underset{\underset{{{geometrical}\mspace{14mu}{range}}{difference}}{︸}}{\rho_{s}^{i} - \rho_{r}^{i}} + \underset{\underset{{{time}\mspace{14mu}{difference}}{{between}\mspace{14mu}{clocks}}}{︸}}{c\left( {{dt}_{s} - {dt}_{r}} \right)} + \underset{\underset{{{integer}\mspace{14mu}{ambiguity}\mspace{14mu}{in}}{{phase}\mspace{14mu}{measurement}}}{︸}}{\lambda\left( {N_{s}^{i} - N_{r}^{i}} \right)} + {\left( {ɛ_{\phi,s} - ɛ_{\phi,r}} \right).}}$

Note that any timing error in the transmitter does not appear in theseobservables and thus allows position solutions even when the system isasynchronous or imperfectly synchronized. In addition, any troposphericdelay error in measurements nearly cancels out since the troposphericdelay is likely to be correlated in the local area for short baselines(i.e., distances between reference receiver r and receiver s). Acommunication channel is used to send the range and carrier measurementsfrom the reference receiver r to the receiver s for positioncomputation. Or, alternatively, the receiver s and receiver r need tocommunicate the range and carrier to the server for positioncomputation.

In any position solution method, the height of a receiver can bedetermined using placement on a terrain map or barometric sensing. Usingplacement on a map, during trilateration the location of the user can beconstrained to be on a terrain based on a terrain database and theheight of the user determined. The height of the user can also beconstrained to be within a certain height above the terrain. Forexample, based on the tallest building in the area, the maximum altitudeabove terrain can be constrained. This type of constraint can improvethe quality of the height solution (for example, by eliminating theambiguous solution that is sometimes produced when using biased rangemeasurements).

In addition, if indoor building maps are available, the information(along with associated constraints on possible user locations) can beused to aid the position solution For example, physical restrictions canbe used to constrain the user motion model, and thereby improve thequality of the tracking Kalman position filter. Another usage ofbuilding maps is to determine/estimate the quality of a particulartower's range measurement based on the physical environment from thetower to the indoor location. A better estimate of range quality can beused to weight the position computation leading to better positionestimates.

When using a barometric sensor, a calibrated barometric sensor can beused to measure the pressure differences as the receiver terminal ismoved up or down in altitude. This is compared with a calibrated valuefor the pressure on different altitudes or an average value to determinethe height of the receiver.

In computing the position solution, when additional measurements greaterthat the minimum three measurements required for two-dimensionalposition are available, receiver integrity monitoring based on a checkof consistency of measurements is used to eliminate “outlier”measurements. The “outlier” measurements could be due to loss of timingsynchronization at the transmitter or due to the channel effects such asmultipath.

Altimeter-Based Approach for Determining Elevation

The WAPS system of an embodiment includes altimeters (pressure sensor)to aid in the determination of user elevation. The only informationavailable from a pressure sensor is the atmospheric pressure at the timeand place of the measurement. In order to translate this into anestimate of the elevation of the sensor, a number of additional piecesof information are required. There is a standard formula for relatingpressure to elevation, based upon the weight of a column of air, asfollows:

${z_{1} - z_{2}} = {{- \frac{RT}{g}}{\ln\left( \frac{P_{1}}{P_{2}} \right)}}$where z₁ and z₂ are two elevations, and P₁ and P₂ are the pressures atthose elevations, and T is the temperature of the air (in K). R=287.052m²/Ks² is the gas constant and g=9.80665 m/s² is the acceleration due togravity. Note that this formula provides relative information,determining the difference in elevation for a difference in pressure.This formula is generally used with z₂=0, so that P₂ is the sea levelpressure. Because sea level air pressure varies significantly withweather conditions and with location, the sea level pressure is neededin addition to the temperature and pressure at the site where elevationis to be determined. When applying standard atmosphere conditions, withT=15 C and P=101,325 Pa, it is found that a 1 m increase in elevationcorresponds to a 12.01 Pa decrease in pressure.

Thus, to determine elevation with a resolution of 1 m, sea levelpressure must be known with accuracy significantly finer than 36 Pa. Itis also worth noting that because T is measured in Kelvin, a 3° C. (orK) error in temperature will correspond to approximately a 1% error inelevation. This can become significant when determining elevationsignificantly above sea level, and when trying to resolve upper floorsin a high rise building. Thus, for determining elevation with aresolution of 1 m, pressure sensors with high accuracy and resolutionare needed. In order to fit in a mobile device, these sensors should below cost, low power and small size. Note that commercial weather gradesensors do not provide this level of accuracy or resolution and are notupdated at a rate required for determining elevation.

The key to determining elevation to 1 m accuracy is to have a system forproviding reference pressure information that is local enough andaccurate enough. It must be able to provide measurements that are closeto the unknown location in temperature, and close in distance andtime—to capture changing weather conditions; and finally, must besufficiently accurate. Thus, the elevation determining system of anembodiment includes but is not limited to the following elements: amobile sensor that determines pressure and temperature at the unknownlocation with sufficient accuracy; an array of reference sensors thatdetermine pressure and temperature at known locations with sufficientaccuracy, and are sufficiently close to the unknown location; aninterpolation-based estimation algorithm which inputs all referencesensor data, reference sensor locations and other augmentinginformation, and generates an accurate reference pressure estimation ata location of interest within the WAPS network; a communications linkbetween the reference sensors and the mobile sensors to provide thereference information in a sufficiently timely fashion. Each of theseelements is described in detail below.

FIG. 36 is a block diagram of a reference elevation pressure system,under an embodiment. Generally, the reference elevation pressure system,or reference system, includes a reference sensor array comprising atleast one set of reference sensor units. Each set of reference sensorunits includes at least one reference sensor unit positioned at a knownlocation. The system also includes a remote receiver comprising orcoupled to an atmospheric sensor that collects atmospheric data at aposition of the remote receiver. A positioning application running on aprocessor is coupled to or is a component of the remote receiver. Thepositioning application generates a reference pressure estimate at theposition of the remote receiver using the atmospheric data and referencedata from the reference sensor unit(s) of the reference sensor array.The positioning application computes an elevation of the remote receiverusing the reference pressure estimate.

More specifically, the reference elevation pressure system includes amobile sensor that determines pressure and temperature at the unknownlocation with sufficient accuracy, and the mobile sensor is a componentof or coupled to the remote receiver. The system includes a referencesensor array that comprises at least one reference sensor unit thataccurately determines pressure and temperature at a known location thatis appropriate to a location of the remote receiver. The referencesensor units communicate with the remote receiver and/or an intermediatedevice (e.g., server, repeater, etc.) (not shown) to provide thereference information. The system comprises a positioning applicationthat, in an embodiment, is an interpolation-based estimation algorithmwhich inputs all reference sensor data, reference sensor locations andother augmenting information, and generates a relatively accuratereference pressure estimation at a location of interest. The positioningapplication can be a component of the remote receiver, can be hosted ona remote server or other processing device, or can be distributedbetween the remote receiver and a remote processing device.

FIG. 37 is a block diagram of the WAPS integrating the referenceelevation pressure system, under an embodiment. As described herein, theWAPS includes a network of synchronized beacons, receiver units thatacquire and track the beacons and/or Global Positioning System (GPS)satellites (and optionally have a location computation engine), and aserver that comprises an index of the towers, a billing interface, aproprietary encryption algorithm (and optionally a location computationengine). The system operates in the licensed/unlicensed bands ofoperation and transmits a proprietary waveform for the purposes oflocation and navigation purposes. The WAPS system can be used inconjunction with other positioning systems or sensor systems in order toprovide more accurate location solutions. Note that the elevation of theremote receiver computed using the reference pressure estimate can beused either explicitly as an altitude estimate or implicitly to aid theposition calculation in any position location system.

One example system integrates the reference elevation pressure systemwith the WAPS. Generally, the integrated system comprises a terrestrialtransmitter network including transmitters that broadcast positioningsignals comprising at least ranging signals and positioning systeminformation. A ranging signal comprises information used to measure adistance to a transmitter broadcasting the ranging signal. The systemincludes a reference sensor array comprising at least one referencesensor unit positioned at a known location. The remote receivercomprises or is coupled to an atmospheric sensor that collectsatmospheric data at a position of the remote receiver. A positioningapplication running on a processor is coupled to or is a component ofthe remote receiver. The positioning application generates a referencepressure estimate at the position of the remote receiver using theatmospheric data and reference data from a set of reference sensor unitsof the reference sensor array. The positioning application computes theposition of the remote receiver, which includes an elevation, using thereference pressure estimate and information derived from at least one ofthe positioning signals and satellite signals that are signals of asatellite-based positioning system.

More specifically, this integrated system includes a mobile sensor thatdetermines pressure and temperature at the unknown location withsufficient accuracy. The mobile sensor is a component of or coupled tothe remote receiver, but is not so limited. The system includes areference sensor array that comprises at least one reference sensor unitthat accurately determines pressure and temperature at a known locationthat is appropriate to a location of the remote receiver. The referencesensor units communicate with the remote receiver and/or an intermediatedevice (e.g., server, repeater, etc.) (not shown) to provide thereference information. The reference sensor units can be collocated withone or more WAPS transmitters and/or can be separately located at otherknown locations. The system comprises a positioning application that, inan embodiment, is an interpolation-based estimation algorithm whichinputs all reference sensor data, reference sensor locations and otheraugmenting information, and generates a reference pressure estimation ata location of interest. The positioning application can be a componentof the remote receiver, can be hosted on the WAPS server or otherprocessing device, or can be distributed between the remote receiver andthe WAPS server.

As noted above, the mobile sensor should be able to determine pressurewith a resolution and accuracy that is significantly finer than 36 Pa,Many pressure sensors have built-in temperature sensors in order toprovide compensation for non-ideal sensor performance, but due toself-heating effects, these sensors may not provide a sufficientlyaccurate measure of outside air temperature. Even in cases whereaccurate sensors are not available commercially, if sensors withadequate resolution are available, they can be used for the purposes ofaltitude estimation at the floor level. The mobile sensor of anembodiment determines the reference pressure data with a resolutionapproximately less than 36 Pascal, and determines the temperature datawith a resolution at least one of equal to and less than approximately 3degrees Celsius.

These sensors have inherent short term and long term stability issueswhich may be corrected by modest filtering techniques such as averaginga few samples. Each sensor may also have an offset that may vary withtemperature which needs to be calibrated or compensated by means of alook up table, for example.

With sufficient calibration, these sensors should provide the accuracyneeded. Some sensors may also be sensitive to high rates of motion. Someheuristic rules may be used to limit use of pressure information whenhigh velocities or acceleration are recognized. However, high velocitiesare rarely experienced in indoor environments. When traveling at highspeeds, GPS positioning and map data will typically provide sufficientvertical position information.

It should also be noted that the sensor should be mounted in a mannerthat exposes it to outside air, but not wind, draft, or other airmovement. A mounting or positioning internal to a typical consumerproduct should produce acceptable results. The battery compartment andconnectors provide an indirect path for outside air to get to thesensor, while preventing any direct air movement. However, a water proofdevice would need special provisions to provide the sensor with accessto the outside.

The reference sensors will be deployed in much smaller volumes, and atdedicated sites, so relatively better accuracy can be obtained in thereference system, making it possible to allocate the bulk of the overallerror budget to the mobile sensors. Existing markets for absolutepressure sensors, such as weather and aircraft altimeters, do not havethe same high accuracy requirements as the application of an embodiment.In the reference application, an embodiment uses multiple sensors, bothfor redundancy and for improved accuracy by averaging theirmeasurements. In addition, the sensors may be packaged so as to limitthe temperature range to which the sensor is exposed and optimallycalibrate the sensor for this limited temperature range.

The reference system should average or otherwise filter individualmeasurements to improve accuracy with a time scale in the order of a fewseconds to a few minutes. The height of the reference sensor should bemeasured to a ‘cm’ level accuracy; the outside air temperature should becontinuously measured and logged; the sensor should be exposed tooutside air in order to measure the air pressure, but must not besubject to wind, drafts, or other significant air movement (baffles orother packaging can be used to direct air along an indirect path to thesensor); the sensor should not be sealed in a water proof enclosure, asthis can prevent measurement of outside air pressure. The referencesensor of an embodiment determines the reference pressure data with aresolution approximately less than 36 Pascal, and determines thetemperature data with a resolution at least one of equal to and lessthan approximately 3 degrees Celsius.

An embodiment enables interpolation-based reference pressure estimation.Given the pressure and temperature measurements at each WAPS transmittertower, as well as the tower location and other augmenting information,an embodiment predicts the sea level atmospheric pressure at the mobileuser location as the reference value for user height estimation.Therefore, an atmospheric pressure surface gradient model is generatedand the pressure measurements at each tower site serve as the sampledata for local modification of the model. Therefore, this estimationalgorithm calibrates comparable reference pressure accuracy at the userlocation as the direct measurements captured at the beacon tower.

A description of a formulation of this interpolation is described below.Within one of the WAPS network, given reference barometric pressuresensors at n transmitter towers, the equivalent sea level atmosphericpressure is estimated based on the reference sensor outputs. This isdone in two steps, but is not so limited.

As a first step, given the reference sensor height h_(i) (in meters)above sea level at transmitter tower i, and the pressure p_(i) (inPascal) and temperature T_(i) (in Kelvin) readings from the referencesensor, the equivalent sea level atmospheric pressure P_(i) (in Pascal)is calculated at location with latitude x_(i) and longitude y_(i) (indegrees), using the formula below:

$P_{i} = {p_{i}e^{\frac{{gh}_{i}}{{RT}_{i}}}}$where g is the gravitational acceleration constant and R is the specificgas constant for air. As a second step, after calculating the equivalentsea level atmospheric pressures at all n transmitter locations of theWAPS network, and obtaining the latitude x₀ and longitude y₀ informationof the user with WAPS, the equivalent sea level pressure is estimated atthe user location P₀ with the formula below:

$P_{0} = {\sum\limits_{i = 1}^{n}{W_{i}P_{i}}}$where W_(i)=W_(i)(x₀, y₀, x_(i), y_(i)) is the weighting functiondepending on both the user location and the reference site i location.

The communications link of an embodiment provides the information usedby the mobile sensor. An embodiment broadcasts pressure updates onceevery few seconds to few minutes but is not so limited.

If the reference system broadcasts reference information infrequently,the mobile unit performs at least one of the following: continuouslymonitors the broadcasts to receive and store the last information incase it is needed before the next broadcast; waits for the nextbroadcast before computing a new elevation; “pulls” or queries thereference system for the latest information when needed. The Pullapproach of an embodiment, rather than having the reference systemsbroadcast the information, minimizes system bandwidth. However, the Pulluses two-way communications between the reference system and the mobile,and since multiple reference sites would be used for any mobilecalculation, so it requires the mobile to determine which referencesites it should query. A good compromise to minimize monitoring by themobile, while keeping latency low, has the reference system broadcastits data more frequently than the time it takes to update themeasurement.

An embodiment includes two possible approaches for the informationcontent. A first approach has the mobile perform all of thecalculations, in which case the information sent by the referenceincludes but is not limited to the following: reference location(latitude and longitude) with one meter accuracy; height of referencesensor with 0.1-0.2 m accuracy; measured temperature of air at referencesite (after some filtering); measured pressure of air at reference site(after filtering, sensor temperature compensation, and any other localcalibration such as offset), with one Pa accuracy; and a measure ofconfidence.

Alternatively, the reference site can use its temperature and pressuremeasurements to compute an equivalent sea level pressure. If thisapproach is used, the list of information to be broadcast includes butis not limited to the following: reference location (latitude andlongitude) with one meter accuracy; height of reference sensor with0.1-0.2 m accuracy; computed equivalent sea level pressure at referencesite (with one Pa accuracy); a measure of confidence.

An embodiment also reduces the bits of data transmitted but broadcastseach piece of data relative to some known constant. For example, thereference sites are relatively close to the mobile site, so only thefractional degrees of latitude and longitude may be transmitted, leavingthe integer part to be assumed. Similarly, air pressure, althoughtypically on the order of 10⁵ Pascals, only varies by a few thousand Pafrom the standard atmosphere. Thus, an embodiment broadcasts the offsetfrom standard atmospheric pressure to reduce the bandwidth overbroadcasting the absolute pressure.

Latitude and longitude, as obtained from GPS or similar systems, are notparticularly useful in urban applications. Instead a database is neededto map latitude and longitude into street addresses. Elevation has asimilar limitation in the vertical dimension. The useful parameter iswhich floor a person is on. This can be determined accurately fromelevation information if there is access to a database of the groundlevel elevation and the height of each floor in a building. For lowbuildings up to approximately 3 stories, it may be sufficient to knowground level elevation from mapping or similar databases, and estimatefloor height. For taller buildings more accurate information about floorheight will be needed.

This presents an opportunity to implement smart learning algorithms. Forexample, one can assume that cell phones will be carried between 1 m and2 m from the floor. Thus, the system of an embodiment can accumulate theelevations of many cell phones in a building, wherein the data isexpected to cluster around 1.5 m from each floor. With enough data, itis possible to develop confidence as to the height of each floor in thebuilding. Thus, the database could be learned and refined over time.Such an algorithm becomes more complicated in buildings with ramps, ormezzanines between floors, but may still generate useful data for themajority of buildings.

The sensor offsets, and potentially other parameters, can be calibratedat the time of manufacture. This should be possible by cycling thesensors through a range of temperature and pressure with a known goodsensor providing reference information. It is likely that thesecalibration parameters will slowly drift with age. Therefore, anembodiment uses an algorithm to gradually update the calibration overtime (e.g., algorithm recognizes when a sensor is stationary at a knownheight and updates the calibration table under those conditions).

In addition to the general application of determining a person'slocation, an embodiment may include specialized applications that usemore precise relative elevation information, while not needing absoluteelevation information. For example, finding a downed firefighter in abuilding requires that the position of the downed person relative to therescue party be known precisely, but neither absolute position is asimportant. Additional precision in relative positioning would bepossible by having an extra manual step at the beginning of theapplication. For example, all firefighters could initialize theretrackers at a known location, such as the entrance to the building,before they enter. Their position relative to that point, and thusrelative to each other could be determined quite accurately for a periodof time, even if absolute elevation is not accurate, and weather relatedpressure changes cannot be completely compensated for. Similarly, ashopping related application that requires more precision than availablefrom the absolute measurements could be implemented by having the userpress a button at a known point in the mall. Their position relative tothat point could then be determined quite accurately for a period oftime.

Alternatively, a mobile beacon can be utilized as a local reference toprovide more accuracy in a particular location. For example, a shoppingmall could have its own reference sensor, to provide more accuracywithin the mall. Similarly, a fire truck could be equipped with areference sensor to provide local reference information at the scene ofa fire.

Low cost pressure sensors have a problem in that they have an offsetfrom the correct reading. Experiments have shown that this offset isquite stable on time scales of weeks to months. However, it is likelythat this offset will slowly drift with time over a period of manymonths to years. While it is straightforward to measure this offset, andcompensate for it at the time of manufacture, it is unlikely that thecompensation will stay accurate for the life of the product. Therefore,a means of recalibrating in the field is required.

The sensor of an embodiment can be recalibrated if it is at a knownelevation and the atmospheric pressure is known. The embodimentidentifies practical situations where the sensor will be at a knownelevation. For example, if the sensor is in a device that has GPScapability, and the GPS satellites are being received with high signalstrength, the GPS derived altitude should be quite accurate.Accumulating the deviations from GPS altitude over time, under goodsignal conditions, can provide an estimate of the correction needed tothe sensor calibration.

Similarly, the sensor system can learn the user's habits and use thisinformation to later correct the calibration. For example, if the userconsistently places her phone in one place at night, the sensor canstart tracking the altitude at this location, perhaps at specific times,such as late night. Initially, these values would be accumulated andstored as the true altitude at that location. After several months, whenthe sensor determines that it is in the same location at the same timeof night, it could start to track deviations from the true altitudedetermined earlier. These deviations could then be accumulated to slowlygenerate a correction to the calibration. Because these approaches alsouse knowledge of current atmospheric pressure, they use referencepressure measurements provided by the WAPS network.

The standard process for determining altitude from pressure readingsinvolves converting the measurements at a reference location to theequivalent sea level pressure, and then using that to determine thealtitude of the unknown pressure sensor. The standard formula is:

$z = {{- \frac{RT}{g}}{\ln\left( \frac{P}{P_{0}} \right)}}$Note that a minus sign has been added, since height is conventionallymeasured as positive moving away from the surface of the earth. Inaddition, the logarithm has been corrected to ‘ln’ since this is anatural logarithm. This formula relates, z, the height above sea level,to the atmospheric temperature (T) and pressure (P) at that point, andthe sea level air pressure (P₀) below that point.

One additional problem with applying this formula is that the height isdirectly proportional to the temperature, a measured quantity not knownprecisely. This means that a 1% error in temperature will result in a 1%error in height. When used near sea level this will not be a significantproblem. However, when this formula is applied in tall buildings andespecially in higher elevation areas, such as Denver, a 1% error inheight may be significant when attempting to resolve floor levelelevation. For example, the elevation of Denver is about 1608 m. Thus, a1% error in temperature will result in an error in height above sealevel of 16 m. This is nearly 5 floors.

One way to avoid this sensitivity to temperature accuracy is torecognize that the formula above is actually a relative formula. That isthe formula can be generalized to:

${z_{1} - z_{2}} = {{- \frac{RT}{g}}{\ln\left( \frac{P_{1}}{P_{2}} \right)}}$where z₁ and z₂ are any two elevations, and P₁ and P₂ are the pressuresat those elevations. It was only a matter of convention that z₂ was setto 0, and thus P₂ became the sea level pressure.

Instead of using sea level as the reference point, any convenientelevation could be used. For example, the mean elevation of the citywould be reasonable, or the mean elevation of the reference sensors usedfor collecting pressure data would work. As long as a referenceelevation is used that keeps the height differences small, the impact oftemperature error will be insignificant. The only requirement is thatall devices involved in the system know what reference elevation isbeing used.

There is a standard formula that relates elevation of a point above theearth (z), the atmospheric temperature (T) and pressure (P) at thatpoint, and the sea level air pressure (P₀) below that point as

$z = {\frac{RT}{g}{\ln\left( \frac{P}{P_{0}} \right)}}$This formula assumes that there is a column of air at constanttemperature between sea level and the point of interest. Therefore, thesea level pressure used is a virtual construct, and not necessarily thereal pressure at sea level, since the point of interest may not be neara true sea level.

The standard process for determining elevation of an object is a twostep process. First sea level pressure is determined by measuringtemperature and pressure at a point of known elevation, and theninverting this formula to solve for P₀. Next, the temperature andpressure at the point of unknown elevation are measured, and thisformula is applied to determine the unknown elevation.

Implicit in this process is the assumption that only parameter ofinterest is the height of other objects above the same horizontallocation, as is typical for aircraft approaching an airfield, usingmeasurements at the airfield for reference. Typically, people interestedin height determination for other purposes have extended this concept todetermining the height in the general vicinity of a reference location,but not directly above it. This extension assumes that the sea levelpressure does not change between the location of interest in thevicinity and the reference location.

Thus, there are three assumptions in this process. A first assumption isthat the temperature is constant from the reference location to thevirtual sea level point below it. A second assumption is that thetemperature is constant from the point of interest to the virtual sealevel point below it. A third assumption is that the sea level pressureis the same at the reference location and the point of interest.However, since sea level pressure depends upon temperature, assumingthat the sea level pressure is the same at two locations implies thatthe temperature is the same at those locations. Thus, if differenttemperatures are measured at the reference location and point ofinterest, one of these assumptions has been violated. Measurements haveshown that even over distances of a few kilometers, there aredifferences in temperature and in pressure that can be significant forelevation determination.

The assumption of constant temperature over elevation changes at a givenlocation is part of the equilibrium model for the atmosphere, and isprobably necessary. The only alternative would be a full dynamic modelof the atmosphere, including the effects of wind, surface heating,convection, and turbulence. Atmospheric data suggest that at least onlarge distance scales, the constant temperature model is a very goodapproximation at elevations below 1 km. At higher elevations, a linearlapse rate is often applied.

An embodiment relaxes the assumption of constant sea level pressurebetween the reference location and the point of interest. A firstapproach of an embodiment takes the sea level pressure for the referencelocation determined as above, but further applies the ideal gas law toconvert this to a sea level pressure at a standard temperature. Thenassume that this sea level pressure at a standard temperature would bethe same at the point of interest. The temperature at the new locationwould then be used to convert this to the sea level pressure for thatlocation, and then apply the formula above to determine the elevation.

A second approach of an embodiment uses a network of reference locationsto determine the variation of equivalent sea level pressure withhorizontal location in real time. These multiple measurements are thencombined to determine a best estimate of the sea level pressure at thepoint of interest. There are at least two possible ways of determiningthe best estimate: a weighted average approach in which the weighting isa function of the horizontal distance from the particular referencepoint to the point of interest; a least square fit to create a secondorder surface that best fits the computed sea level pressures at thereference locations and can then be used to interpolate an estimate ofthe sea level pressure at the point of interest.

The two approaches described above can also be combined. That is, ateach reference location the sea level pressure at standard temperatureis determined, and these data are combined using one of the techniquesabove to generate a best estimate of the sea level pressure at standardtemperature at the point of interest.

Additionally, when using the altimeter, an embodiment recognizes suddenmovements in pressure such as the air conditioner changing state (e.g.,turning ON, etc.) or windows opening in a car by using application leveldata into the hardware or software filters that operate continuously onthe location and altimeter data.

Further, a wind gauge can be used at the beacon to determine thedirection of the wind flow, which is believed to be a indicator ofatmospheric pressure gradient. A wind gauge along with a compass can beused to determine the precise direction and level of wind flow which canthen be used to correct and/or filter our variations in the user'ssensor.

The per floor height of a given building can be determined by variousmethods including but not limited to a user walking the building throughthe stairs and collecting information about each floor, ramps etc. Inaddition an electronic diagram can be used to determine the relativeheight of each floor.

When the height is estimated based on either WAPS or the altimeter,information such as terrain, height of the building, height ofsurrounding buildings, etc. can be used to constrain the heightsolution.

Once an average pressure is known at a given location, along withhistorical reference pressure data collected from the reference sensorsover a long period of time (days, months, year), it can be used topredictably determine the height based on the pressure at that location(without calibration or user input).

In one embodiment, the height of the user can be computed on a remoteserver by using the data from the user's sensor and combining it withthe data from reference sensors. In this method, other information suchas building information, crowd sourced information, etc. can also beused to determine the user's precise altitude.

In case a user is in close proximity to another user whose height isknown, this information can be used to determine the unknown user'sheight.

In one embodiment of the network, the reference sensors need notnecessarily be co-located with the WAPS beacon. A finer or a coarsergrid of independent sensors with data connection to the server can beused for reference pressure measurement. The centralized server caneither send reference pressure information to the mobile or can instructthe transmitters with data that needs to be sent to the mobile as a partof the WAPS data stream.

In another embodiment, the WAPS system uses an additional simplifiedbeacon (supplemental beacon) that provides additional sensor informationsuch as pressure, temperature in a smaller area such as a building. Thistransmission may be synchronous or asynchronous to the main WAPS timingbeacons. Additionally, the supplemental beacon may either upload thesensor data to a centralized server from which it is disseminated to themobile units or transmit the data over a predefined set of PRN codeswhich can be demodulated by the WAPS mobile receiver.

The reference pressure network can be optimized based on accuracyrequirements and historic pressure variation data for a given localarea. For example, in cases where very accurate measurement is a must, areference sensor can be deployed in that building or a mall.

The WAPS beacon network along with the reference pressure data forms aclose network of accurate pressure and temperature measurement with veryshort time intervals which can be harnessed by other applications suchas geodesy.

The rate of change of pressure combined with data from other sensors canbe used to determine vertical velocity which can then be used todetermine if a user went through an elevator. This can be very useful inemergency situations and/or tracking applications.

In cases of sensors with lower resolution than needed to estimate floorheight, under static conditions, averaging the pressure measurementsover time can be used to obtain the user height based on reference data.

Hybrid Positioning and Information Exchange with Other Systems

The system of an embodiment can be combined with any ‘signal ofopportunity’, in order to provide positioning. Examples of a signal ofopportunity include, but are not limited to, one or more of thefollowing: GPS receivers; Galileo; Glonass; Analog or Digital TV Signal;signals from systems such as MediaFLO, Wi-Fi; FM signals; WiMax;cellular (UMTS, LTE, CDMA, GSM etc); bluetooth, and, LORAN and e-LORANreceivers.

Regardless of signal type, the signal of opportunity provides a rangemeasurement or a proxy for a range measurement, such as signal strength.This proxy for a range is weighed and combined appropriately to get anestimate for the location. The weighting may use the signal-to-noiseratio (SNR) of the received signals or, alternatively, use a metric thatdefines the environment of the receiver (e.g., knowledge of urban,suburban, rural environment from assistance data, whether the receiveris indoor or outdoor based on input from the application). This istypically done in those environments where the system of an embodimentis unavailable or signal coverage is limited. When using the SNR for aweight for a particular measurement the weight may simply be an inversefunction of the SNR (or any other function that provides lower weight tosignals with lower SNR) to allow optimal combination of the WAPSmeasurements as well as other system measurements to obtain a position.The final positioning solution may be calculated either by taking rangemeasurements from the additional signal sources and combining with theWAPS range measurements and deriving a position solution for latitude,longitude and height, or by taking the position measurements from theadditional sources/devices and the position measurements from the WAPSsystem and providing an optimized location solution using a combinationof these location measurements based on the position quality metric fromdifferent systems. The various configurations of obtaining a hybridsolution using WAPS measurements/WAPS position estimates are shown inFIG. 38, FIG. 39, and FIG. 40. Any of the architectures described belowcan be selected for use depending on the hardware and softwarepartitioning of the system.

FIG. 38 is a block diagram of hybrid position estimation using rangemeasurements from various systems, under an embodiment. The rangemeasurements (along with associated range quality metrics) are used fromGNSS and other positioning systems and combined in a single optimalposition solution by a hybrid position engine. This architecture is themost optimal in terms of using the available data to get the bestposition estimate out of them.

FIG. 39 is a block diagram of hybrid position estimation using positionestimates from various systems, under an embodiment. Independentposition estimates from different systems along with position qualityare used to choose the one with the best quality. This architecture isthe easiest to implement and integrate since the different positioningsystem are well isolated.

FIG. 40 is a block diagram of hybrid position estimation using acombination of range and position estimates from various systems, underan embodiment. For example, a position estimate from a WLAN positioningsystem can be compared with position estimate from range measurementsfrom GNSS and WAPS systems to arrive at the best solution.

Inertial Navigation Sensors (INS) such as accelerometers and gyros,magnetic sensors such as e-compass, pressure sensors such as altimeterscan be used to provide location aiding information (referred to as loosecoupling) or raw sensor measurements (referred to as tight coupling) tothe WAPS system for usage in tracking mode.

An accelerometer can be used in the receiver of an embodiment todetermine a frequency for updating the position reporting to the server.A combination of sequence of position solutions and accelerometermeasurements can be used to detect static position, constant velocityand/or other movement. This movement data or information can then beused to determine the frequency of the updates such that, for example,when there is non-uniform motion the frequency of updates can be set toa relatively high frequency, and when the receiver is at a constantvelocity or stationary for a pre-determined period of time the frequencyof the updates can be reduced to save power.

The sensor or position measurements can be combined into a positionsolution in a position filter (such as a Kalman filter). Two types oftight coupling architectures, where the sensor measurements are combinedwith GNSS and WAPS measurements in the WAPS hybrid position engine, areillustrated in FIG. 41 and FIG. 42. FIG. 41 is a flow diagram fordetermining a hybrid position solution in which position/velocityestimates from the WAPS/GNSS systems are fed back to help calibrate thedrifting bias of the sensors at times when the quality of the GNSS/WAPSposition and/or velocity estimates are good, under an embodiment. Thisarchitecture simplifies the algorithm formulation by partitioning thesensor calibration and position calculation parts of the algorithm.However, the drawback of this method is the complexity in deciding whenare the good times to re-calibrate the sensors using WAPS/GNSSestimates.

FIG. 42 is a flow diagram for determining a hybrid position solution inwhich sensor parameters (such as bias, scale and drift) are estimated aspart of the position/velocity computation in the GNSS and/or WAPS unitswithout need for explicit feedback, under an embodiment. For example,the sensor parameters can be included as part of the state vector of theKalman filter used for tracking the position/velocity of the receiver.This architecture provides an optimal solution in that the informationis used in one combined filter to update both position and sensorparameters.

Loose coupling is illustrated in FIG. 43 and FIG. 44 where a selectionunit selects between position estimate from the GNSS engine and the WAPSengine. Note that the selection unit may be part of the WAPS or GNSSposition units. FIG. 43 is a flow diagram for determining a hybridposition solution in which sensor calibration is separated from theindividual position computation units, under an embodiment. FIG. 44 is aflow diagram for determining a hybrid position solution in which thesensor parameter estimation is done as part of the state of theindividual position computation units, under an embodiment.

The loose coupling methods are generally worse than the tight couplingmethods since a selection uses information only from one system. Amongstloose coupling or tight coupling methods, the method that uses theranges along with raw sensor measurements to determine position andsensor parameters in one optimal filter are better than when sensorparameters and position are computed separately. As a result, thepreferred method from a performance perspective is the tight couplingsystem with implicit sensor parameter estimation. However, depending onthe hardware/software platform partitioning, one or more of thesemethods may be easily implemented and may be selected for that reason.

Information can also be exchanged between the WAPS system and othertransceiver systems on the same platform (such as cell-phone, laptop,PND). The transceiver systems can be, for example, Bluetoothtransceiver, WLAN transceiver, FM receiver/transmitter, digital oranalog TV system, MediaFLO, satellite communication system such as XMradio/Iridium, Cellular modem transceivers such as GSM/UMTS/cdma20001×/EVDO or WiMax). FIG. 45 shows the exchange of information between theWAPS and other systems, under an embodiment. The exchange of informationbetween systems can improve the performance of either system. Since theWAPS system time is aligned to GPS time, the WAPS system can providegood quality timing and frequency estimates to any other system. Timeand frequency estimates into the WAPS system can reduce the WAPSacquisition search space in code and frequency. In addition, the WAPSsystem can provide location information to the other transceiversystems. Similarly, if the other system has location information(partial position e.g., Altitude or 2-D position, or full position e.g.,3-D position or raw range/pseudo-range/range-difference) available, thatlocation information can be provided with or without a location qualitymetric to the WAPS system. The range/pseudo-range data should beprovided along with the location of transmitter (or other means tocompute the range from the transmitter location to any receiverlocation) to enable usage of this range information in a hybridsolution. The range difference corresponding to two transmitters shouldbe provided along with location of the two transmitters. The WAPS systemwill use the information to aid its position solution. Alternatively,location information can be provided in the form of ranges (orpseudo-ranges) from known transmitter locations to the receiver device.These ranges (or pseudo-ranges) would be combined with WAPS ranges bythe positioning algorithm to compute a hybrid position.

Examples of specific systems and information that can be exchangedbetween them are shown in FIG. 46, FIG. 47, and FIG. 48.

FIG. 46 is a block diagram showing exchange of location, frequency andtime estimates between FM receiver and WAPS receiver, under anembodiment. The location estimates from WAPS system can be provided toan FM Receiver. This location estimate may then be used, for example, toautomatically determine active FM radio stations in the local region.The FM signal may include a RDS—Radio Data Service) transmission aswell. If the location of the FM station is included in the RDS/RBDSdata-stream (for example, the Location and Navigation (LN) feature thatprovide data about the transmitter site, giving city and state name andprovide DGPS navigation data) then this information can be used toprovide location aiding to the WAPS Receiver. The frequency estimatefrom the WAPS system can be easily used to reduce the FM Receiver tuningtime for a particular station. In the other direction, the frequencyquality of the estimate in the FM Receiver is based on the FM radiostation transmit quality. The time estimate in the WAPS system is basedon GPS time and time can be transferred to the FM Receiver to aid timingalignment. Clock Time (CT) feature on RDS/RBDS transmissions may be usedto determine timing relative to the RDS data stream and can betransferred to the WAPS receiver.

FIG. 47 is a block diagram showing exchange of location, time andfrequency estimates between WLAN/BT transceiver and WAPS Receiver, underan embodiment. In general, these WLAN/BT transceivers do not have anaccurate frequency estimate and as a result the frequency estimateswould be quite coarse, so the transfer of such an estimate from WLAN/BTtransceiver to WAPS receiver may have limited value. In the reversedirection, a WAPS frequency estimate can reduce the time taken forfrequency acquisition on the WLAN system. The timing information that isextracted, for example, from the timestamp on the wireless LAN AP(Access Point) beacons can be transferred to the WAPS system to aid WAPSacquisition. Note that some reference of the WLAN timing relative to GPStime is needed to make this useful for the WAPS system. Similarly, ifthe WLAN/BT system has a location estimate (partial position e.g.,Altitude or 2-D position, or full position e.g., 3-D position or rawrange/pseudo-range) available, that location information can be providedwith or without a location quality metric to the WAPS system. The WLANposition estimate could simply be the geo-location of the serving AP orother “audible” APs in the vicinity. The WLAN position estimate couldalso be partial, for example, the altitude estimate based on the floorof the AP in question. The WLAN location information can also be a rangeestimate to a known transmitter AP location (for example, the WLANsystem may use Round Trip Time measurements to determine range estimate)or a range difference estimate between two transmit APs.

FIG. 48 is a block diagram showing exchange of location, time andfrequency estimates between cellular transceiver and WAPS receiver,under an embodiment. Location estimates (partial, complete or rawranges/range-differences) from cellular systems (such as from TDOA, AFLTor other similar cellular signal FL or RL based positioning method) canbe provided to the WAPS system which will use these measurements toobtain a better position estimate. Frequency estimates from thefrequency tracking loops of the cellular modem can be provided to theWAPS system to reduce the frequency search space and thus improve WAPSacquisition time (i.e. TTFF). Time estimates from the cellular systemcan also be provided to the WAPS system to reduce the code search spaceor to aid bit and frame alignment. For example, systems that aresynchronized to GPS time such as cdma2000/1×EVDO can provide fine timeestimates for the WAPS system whereas asynchronous (transmissions notsynchronized finely to time scale such as GPS) cellular systems such asGSM/GPRS/EGPRS/UMTS may provide coarse time estimates.

Since the WAPS system time is aligned to GPS time, the WAPS system canprovide good quality timing and frequency estimates to any other systemeven if not on the same platform. For example, the WAPS system can beused to provide timing information to a pico/femto-cell BTS through aperiodic hardware signal such as a pps (pulse-per-sec) aligned with GPSsecond-boundaries or a single pulse signal with an associated GPS time.

As described above, the spectrum used by the WAPS system of anembodiment can include licensed or unlicensed bands or frequencies.Alternatively, the WAPS system can use the “White Space” spectrum. Thewhite space spectrum is defined as any spectrum that the WAPS systemssenses or determines to be free in a local area (not limited to TV WhiteSpace) and transmits location beacons in that spectrum. The transmittersof an embodiment can use spectrum-sensing technology to detect unusedspectrum and/or communicate geo-location (can be readily obtained fromthe GPS timing receiver) to a centralized database that coordinates thespectrum. The receivers can include spectrum-sensing technology tolisten to these beacons, or in another embodiment, may be notified ofthe frequency to which to tune using the communication medium. The WAPSsystem can adapt to dynamic white space availability or allocation (incases where the transmitters are required to broadcast theirgeo-location to a centralized database which then allocates either thespectrum to transmit in and/or the time duration for which it needs totransmit). The WAPS system can continuously broadcast in this spectrumor can share the spectrum with other systems as controlled by acentralized coordination service for the spectrum. The chipping rate andthe data rate of the WAPS system components can be modified dynamicallyto suit the accuracy requirements and/or signal power and bandwidthavailability at any given time. The system parameters can be sensed bythe receiver or can be communicated to the receiver through thecommunication medium. The transmitters can form a local network or incases of spectrum availability in a wider geographical area, can form acontinuous network.

The transmitter of an embodiment can also coexist with other networks onthe same transmit system in a time-shared fashion. For example, the samespectrum can be used in a time-shared fashion between location and smartgrid applications. The transmitter is a broadcast transmitter using themaximum available power levels and can adjust its power levelsdynamically based on spectrum sensing or as requested by a centralizedcoordinating server. The receiver can employ spectrum sensing or can becommunicated by a communication medium (which can also be a white spacespectrum) of the system parameters and wake up times at that time.

Based on spectrum availability, the WAPS system of an embodiment can useone channel of the TV White space (6 MHz bandwidth) or, if multiplechannels are available, can use the multiple frequency bands for bettermultipath resolution. If adjacent channels are available, channelbonding (e.g., combining adjacent channels) can be used. The increasedbandwidth can be used for better multipath resolution, higher chippingrate for higher accuracy, etc. Alternatively, the available bandwidthcan be used under FDMA to help solve the near far problem and/ormultipath resolution.

White space transmission/reception of WAPS waveforms in two or morewhite-space bands can enable better and faster integer ambiguityresolution for WAPS carrier phase measurements. This will enablerelatively high accuracy (of the order of <1 wavelength) single pointpositioning using WAPS.

The whitespace bandwidth can also be used as a communication channel inthe WAPS (in cases where a reference receiver is used) between thereference receiver at surveyed location and the receiver whose positionis to be found.

When a WAPS system in the licensed band is available in a wide areanetwork, a White-Space based local network of towers can be used toaugment the location accuracies of the WAPS receiver. The receiver canbe designed to listen to both frequencies simultaneously or switchbetween the licensed band and white space band and tune to theappropriate frequencies.

The White-space bands can also be used to send assistance information tothe WAPS, GPS or AGPS systems for location aiding and other assistanceinformation like clock bias, satellite ephemeris etc.

In cases where multiple frequencies with wide separation are available,the WAPS system can be designed to take advantage of the diversity infrequencies to provide better multipath performance.

Correlator Implementation

In any CDMA receiver (or a receiver that uses Pseudo Random codes as apart of the transmit bit stream), correlation of the received signalwith its PRN code is essential. The more parallel correlations that canbe done, the faster is the time to acquire the channel. A brute forceimplementation of a parallel complex correlator architecture for signalsthat use a maximal length sequence of length 1023, input signaloversampled by 2×, is shown in FIG. 49. The even and odd samplescorrespond to the 2× oversampled data. The shift registers get shiftedat the rate of the ‘clk’. The PRN generator generates the reference PRNand gets shifted at the rate of clk/2. The correlation sum at each cycleis calculated using the equation

${{corrsum}\lbrack n\rbrack} = {\sum\limits_{k = 0}^{2045}{{{gcref}\lbrack k\rbrack}*{x\left\lbrack {k - n} \right\rbrack}}}$where x[n] is the complex input, gcref[k] is the PRN reference waveform,and corrsum[n] is the complex output from the correlator. FIG. 49 showsone optimization where the even and odd samples share the samemultiplier and adder trees.

An implementation like the one shown above requires 2046*2*n-input bitsflip flops for the shift registers, 1023 of 1×n-input multiplier and anadder that sums the 1023 products. As an example, if the input bit widthwere 2-bit samples, then 1023 of 1×2 multipliers are required, and 1023of these multiplications would have to be summed in one clock cycle.This could be an onerous implementation in terms of area, timing andpower in hardware. In particular, in an FPGA implementation a bruteforce implementation of the multiplier and adder structure may beimpossible to implement given the limited resources.

An embodiment includes a novel approach to this implementation whichtakes advantage of the structures available in state of the art FPGAs.Modern FPGAs include several configurable logic blocks (CLBs) thatimplement logic and storage elements. The lookup tables that form anessential part of the CLBs can also be reprogrammed as shift registerswith a serial shift in, but have parallel random access to the storageelements. This implementation can also be used in an ASIC implementationas an efficient approach to computing the correlation and as an easymigration path from FPGAs (used to prototyping) to ASICs (for massproduction volumes).

Turning to shift register implementation, particular FPGAs have shiftregister primitives which are mapped onto the CLBs. Some FPGAs have a16-bit shift register while some have a 32-bit shift register mapping.FIG. 50 shows a 32-bit shift register implementation derived from two16-bit shift register primitives with parallel random access readcapabilities. In this example implementation a 16-bit shift registergroup primitive is used to build a 32-bit shift register. 32 of such32-bit shift registers are strung in series to form the 1024-bit shiftregister. The shift operations occur at ‘clk’ rate, and the readoutoperations occur at 32 times the clock rate, as shown in FIG. 51.

The adder tree can also be complex to implement a 1023×n-bit adder. Inthe case of a particular FPGA, a 48-bit DSP slice is available which canbe used as 1023×n-bit sequential adder. The hardware structure for thisimplementation is shown in FIG. 52. The 32 values from the 32 groups ofshift registers are split into 4 groups of 8 additions. In this example,a 2-bit input is used. Each 8-number adder produces a 10-bit outputwhich is then aligned in a 12-bit group in the 48-bit adder. Room isallowed for the growth of the sum. After 32 cycles, the 1024 bit sum isobtained by adding the 4 groups of the 12-bit adders into one 14-bitsum.

Encryption and Security

The overhead information in the system of an embodiment can be encryptedusing an encryption algorithm. This allows users to use the system andbe billed for usage of the system and provide a means to controlinformation security. Keys can be applied to decrypt the signal. Thekeys can be obtained using a PC, wireless network, hardware dongle orcan be burnt into the non volatile memory of the device in a way that itis inaccessible by any unintended sources.

The encryption of an embodiment provides both data security andauthentication. The key components that are secured using encryption arethe transmitters, the receivers and the server communication.Transmitter Authentication includes unambiguously identifyingtransmitters so that malicious transmitters can be rejected. ReceiverAuthentication is such that only authentic receivers should be able toutilize the transmitted information. Receiver Authorization is such thatonly receivers that are authorized (authentic receiver) should bepermitted to operate. Server Communication is encrypted such thatcommunication between the receivers and the server and between thetransmitters and the server has to be secure. User data protection isalso encrypted because location tracking user databases requireprotection from unauthorized access.

Encryption methods of an embodiment can be broadly classified into twotypes: symmetric key cryptography and asymmetric key cryptography.Symmetric Key encryption provides both authentication and encryption,whereas asymmetric key encryption provides authentication of the privatekey owner, since the public key is available to anyone. Symmetric Keyencryption of data is an order of magnitude faster given similarresources. 3DES and AES are examples of symmetric key cryptography. Acombination of both methods is used as part of the encryptionarchitecture of an embodiment.

Over-the-air (OTA) broadcast messages can comprise general broadcastmessages or system messages. General broadcast messages contain dataspecific to each transmitter such as location information, transmittertiming counts and other pertinent information that assist a receiver indetermining its location. System messages are used to configureencryption keys, enable/disable receivers or for targeted one-wayprivate information exchange to a specific set of receivers.

The general format of a message of an embodiment includes: Message type(parity/ECC protected); Encrypted Message; and Encrypted Message ECC.The ECC for the encrypted message is computed after the message isencrypted.

The OTA broadcast comprises frames that are transmitted periodically,possibly every second. Depending on the channel data rate, a messagecould be split up (segmented) over multiple frames. Each frame comprisesa frame type and frame data. Frame type (parity protected) indicateswhether this is the first frame of a message or if it is a continuingframe; it can also indicate a low level format frame that may be usedfor other purposes. Frame Data is essentially a segmented Message or alow level data frame.

OTA system messages can be encrypted either by the session key or by thetransmitter's private key depending upon the system message type. OTAgeneral broadcast messages are encrypted using a symmetric key algorithmwith a session key that both the transmitter and receiver havenegotiated as described herein. This provides mutual authenticationi.e., transmitters can be authenticated by receivers and onlyauthenticated receivers can decode the OTA broadcast. The session key isknown to all transmitters and receivers and it is changed periodically.Key change messages are encrypted using the past few session keys,allowing receivers that were not active at a certain time period to syncup to the current session key.

OTA broadcasts also include periodic system messages encrypted by thetransmitter's private key. The receivers can unambiguously identify theauthenticity of the transmitter by using the associated public key. Inthe event the session key is compromised, this mechanism ensures thatunauthorized transmitters cannot be implemented.

FIG. 53 is a block diagram of session key setup, under an embodiment.Each receiver is equipped with a unique device ID and a device specifickey. FIG. 54 is a flow diagram for encryption, under an embodiment. TheWAPS System data servers maintain a database of the device ID/devicespecific key pairing. Receiver initialization between a receiver and theWAPS data servers is facilitated using a data connection(GPRS/USB/Modem, etc.) specific to the receiver type. This connection isencrypted using the device specific key after the device identifiesitself with the device ID. During this initialization, the currentsession key, the transmitter public key and licensing terms (i.e.,duration the receiver is authorized) are exchanged. Receiverinitialization can be performed when the receiver has lost the currentsession key (initial power up) or if its session key is out of sync(extended power off). The session key is periodically updated, and thenew key used for the updating is encrypted using the previous N keys.

The OTA data rate may be inadequate for being the sole mechanism toauthorize receivers. However, the system message protocol of anembodiment supports device ID specific and device ID range-basedreceiver authorization.

A compromised session key requires all receivers to re-initialize.Therefore the session key storage should be tamper-proof in the device.Session key stored outside the device crypto boundary (i.e., attachedstorage of any kind) will be encrypted using the device's secure key.

A compromised session key cannot be used to masquerade a transmitterbecause the transmitter periodically transmits authenticationinformation using its private key. Therefore, the transmitter's privatekey should never be compromised.

In an alternative embodiment, shown in FIG. 55, the keys can be directlydelivered to the receiver over the communication link from the WAPSserver or can be routed through a third party application or serviceprovider. The keys can have a certain validity period. The keys can bemade available on a per-application basis or a per device basis based ona contractual agreement with the customer. Every time a position requestis made either by an application on the receiver or by an application onthe network, the keys are checked for validity before retrieving theposition or parameters to compute position from the WAPS engine. The keyand information exchange to a WAPS server can happen using proprietaryprotocols or through standard protocols such as OMA SUPL.

The security architecture of the system can be implemented ascombination of architectures shown in FIG. 53 and FIG. 55.

Parameter sensors can be integrated into receivers of the WAPS system totime tag and/or location tag the measurements from the sensors. Theparameter sensors can include, but are not limited to, temperaturesensors, humidity sensors, weight sensors, and sensors for scanner typesto name a few. For example, an X-ray detector can be used to determineif a tracked receiver, or device including a tracked receiver, passesthrough an X-ray machine. The time of the X-ray event and location ofthe X-ray machine can be tagged by the detector. In addition, otherparameter sensors can be integrated into the WAPS system to both timetag and location tag measurements from the sensors.

Users can be billed for the system on a per use, per application on thedevice, hourly, daily, weekly, monthly and annual basis for anindividual or asset.

The location and height of the receiver unit can be sent to anyapplication on the terminal or to the network server using acommunication protocol. Alternatively, the raw range measurement can besent to the network through a communication protocol. The communicationprotocol can be a standard serial or other digital interface to theapplication on the terminal or through a standard or proprietarywireless protocol to the server. Possible methods of coupling orconnecting to a server through a standard protocol includes the use ofSMS messaging to another phone connected to the server or,alternatively, through a wireless data service to a web server. Theinformation sent includes one or more of latitude/longitude, height (ifavailable), and timestamp. The application on the server or the terminalunit can initiate a position fix. The location of the user can becommunicated directly from the server or by the application on theserver.

The WAPS standalone system independent of a GPS receiver can be used fordetermining the location of a device. The WAPS system by itself orintegrated WAPS and GPS and/or other positioning system can beimplemented to co-exist with media storage cards (such as SD cards) onthe media cards. The WAPS system by itself or integrated WAPS and GPSsystem and/or other positioning systems can be implemented to co-existon a cellular phone Subscriber Identity Module (SIM) card so that theSIM cards can be tracked.

Precise Positioning with Carrier Phase

One method to augment the WAPS system performance to further improveaccuracy (up to <1 m) is to implement a carrier phase positioning systemas described below. The beacons are set up as usual WAPS transmitters.For this method, it may be desirable (but not essential) to not use TDMAslotting to facilitate easy continuous phase tracking. When TDMA is notused, the near-far problem can be overcome through interferencecancellation and increased dynamic range in the receiver. The WAPSreceiver to support such a method is capable of measuring andtime-stamping code and carrier phase in a continuous manner for allvisible satellites. In addition, there is a reference receiver at aknown surveyed location that can also make similar measurements of codeand carrier phase in a continuous manner. The measurements from the WAPSreceiver and the reference receiver may be combined to compute aposition either on the device or on the server. The configuration ofsuch a system would be identical to a differential WAPS system.

Carrier phase measurement is more accurate than code phase measurementbut contains unknown integer number of carrier phase cycles calledinteger ambiguity. However there are ways to find integer ambiguitiescalled ambiguity resolution. One method will be considered here thatuses extension of local minima search algorithm to iteratively solve foruser receiver position and uses measurements at multiple epochs forimproved accuracy.

Consider carrier phase measurement at user receiver at a single epochfirst as follows.ϕ_(u) ^((k))=λ⁻¹ ·r _(u) ^((k)) +N _(u) ^((k))+ƒ·(dt _(u) −dt^((k)))+ε_(u) ^((k))  (1)where ϕ, λ, ƒ and N are carrier phase, wavelength, frequency and integercycles respectively, dt is clock bias, r is range, ε is measurementerror and subscript u represents user receiver k represents transmitternumber.Range is given in terms of user and transmitter positions p_(u) andp^((k)) asr _(u) ^((k)) =∥p _(u) −p ^((k))∥=√{square root over ((p _(ux) −p _(x)^((k)))²+(p _(uy) −p _(y) ^((k)))²+(p _(uz) −p _(z) ^((k)))²)}  (2)To eliminate error in the knowledge of transmitter clock bias consideranother receiver at known position (called reference receiver) withcorresponding carrier phase equationϕ_(r) ^((k))=λ⁻¹ ·r _(r) ^((k)) +N _(r) ^((k))+ƒ·(dt _(r) −dt^((k)))+ε_(r) ^((k))  (3)where subscript r stands for reference receiver and subtract (2) from(1) to getϕ_(u) ^((k))−ϕ_(r) ^((k))=λ⁻¹·(r _(u) ^((k)) −r _(r) ^((k)))+(N _(u)^((k)) −N _(r) ^((k)))+ƒ·(dt _(u) −dt _(r))+(ε_(u) ^((k))−ε_(r)^((k)))  (4)which is written asϕ_(ur) ^((k))=λ⁻¹ ·r _(ur) ^((k)) +N _(ur) ^((k)) +ƒ·dt _(ur)+ε_(ur)^((k))  (5)where (•)_(ur)=(•)_(u)−(•)_(r).Since dt_(u)r is not of interest it can be eliminated by differencing(5) for different values of index (k) to get so called double differenceobservable equationϕ_(ur) ^((kl))=λ⁻¹ ·r _(ur) ^((kl)) +N _(ur) ^((kl))ε_(ur) ^((kl))  (6)where (•)_(ur) ^((kl))=(•)_(ur) ^((k))−(•)_(ur) ^((l)).Equation (6) then is an equation in the unknown user position p_(u)through r_(ur) ^((kl))r _(ur) ^((kl))=(r _(u) ^((k)) −r _(r) ^((k)))−(r _(u) ^((l)) −r _(r)^((l)))=∥p _(u) −p ^((k)) ∥−∥p _(u) −p ^((l))∥−γ^((kl))  (7)whereγ^((kl)) =∥p _(r) −p ^((k)) ∥−∥p _(r) −p ^((l))∥  (8)Typically transmitter l used in double differencing is one of thetransmitters and labeling it as 1 for convenience leads to equation inthe matrix form as

$\begin{matrix}{\begin{bmatrix}\phi_{ur}^{(21)} \\\phi_{ur}^{(31)} \\\vdots \\\phi_{ur}^{(n)}\end{bmatrix} = {{\lambda^{- 1} \cdot \begin{bmatrix}\begin{matrix}{{{p_{u} - p^{(2)}}} - {{p_{u} - p^{(1)}}} - \gamma^{(21)}} \\{{{p_{u} - p^{(3)}}} - {{p_{u} - p^{(1)}}} - \gamma^{(31)}} \\\vdots\end{matrix} \\{{{p_{u} - p^{(n)}}} - {{p_{u} - p^{(1)}}} - \gamma^{({n\; 1})}}\end{bmatrix}} + \begin{bmatrix}N_{ur}^{(21)} \\N_{ur}^{(31)} \\\vdots \\N_{ur}^{({n\; 1})}\end{bmatrix} + \begin{bmatrix}ɛ_{ur}^{(21)} \\ɛ_{ur}^{(31)} \\\vdots \\ɛ_{ur}^{({n\; 1})}\end{bmatrix}}} & (9) \\{\mspace{20mu}{or}} & \; \\{\mspace{20mu}{\phi = {{\lambda^{- 1} \cdot {f\left( p_{u} \right)}} + N + ɛ}}} & (10)\end{matrix}$Equation (10) is a nonlinear equation in unknown user position p_(u).Local minima search algorithm works on linear equations and so (10) islinearized and solved iteratively as follows. Let at iteration m,approximation to p_(u) is p_(u) ^(m) where

$\begin{matrix}{{p_{u} = {p_{u}^{m} + {\Delta\; p_{n}}}}{and}} & (11) \\{{{f\left( p_{u} \right)} = {{f\left( {p_{u}^{m} + {\Delta\; p_{u}}} \right)} \approx {{f\left( p_{u}^{m} \right)} + {\frac{\partial f}{\partial p_{u}}{\left( p_{u}^{m} \right) \cdot \Delta}\; p_{u}}}}}{where}} & (12) \\{{{\frac{\partial f}{\partial p_{u}}\left( p_{u} \right)} = \begin{bmatrix}{l^{(2)} - l^{(1)}} \\{l^{(3)} - l^{(1)}} \\\vdots \\{l^{(n)} - l^{(1)}}\end{bmatrix}},} & (13)\end{matrix}$where l^((k)) is line-of-sight row vector

$l^{(k)} = \frac{p_{u} - p^{(k)}}{{p_{u} - p^{(k)}}}$Then equation (10) is written as,y=G·x·+N+ε  (13)where y=ϕ−λ⁻¹·ƒ(p_(u) ^(m)),

${G = {{\lambda^{- 1} \cdot \frac{\partial f}{\partial p_{u}}}\left( p_{u}^{m} \right)}},$and x=Δp_(u) Equation (13) is linear in x=Δp_(u) and is solved forΔp_(u) using local minima search algorithm given below. Using soobtained solution of Δp_(u) equation (11) is used to get p_(u) atiteration m and then so obtained p_(u) is used as p_(u) ^(m+1) at thenext iteration (m+1). The iterations are continued till Δp_(u) becomessmall enough to decide convergence. At the beginning of iterations p_(u)⁰ can be taken from code phase based solution.

Now consider solving equation (13). Let Q_(dd) be covariance matrix ofdouble difference carrier phase error vector. It is obtained as follows.Variance of error in single difference observable ϕ_(ur) ^((k))=ϕ_(u)^((k))−ϕ_(r) ^((k)) is Q_(u)+Q_(r) where Q_(u) and Q_(r) are respectivecarrier phase error variances which are assumed to be independent oftransmitter k. Variance of ϕ_(ur) ^((kl))=ϕ_(ur) ^((k))−ϕ_(ur) ^((l)) is2·(Q_(u)+Q_(r)) and cross-variance between ϕ_(ur) ^((jl))=ϕ_(ur)^((j))−ϕ_(ur) ^((l)) and ϕ_(ur) ^((kl))=ϕ_(ur) ^((k))−ϕ_(ur) ^((l)), j≠kis Q_(u)+Q_(r) which is variance of the common term ϕ_(ur) ^((l)). So,

$\begin{matrix}{Q_{dd} = {\left( {Q_{u} + Q_{r}} \right) \cdot \begin{bmatrix}2 & 1 & \ldots & 1 \\1 & 2 & \ldots & 1 \\\vdots & \vdots & \ddots & \vdots \\1 & 1 & \ldots & 2\end{bmatrix}}} & (14)\end{matrix}$

Weighted least squares solution of (13) is:{circumflex over (x)}=G ^(L)·(y−N) where G ^(L) is left inverse of G, G^(L)=(G ^(T) ·Q _(dd) ⁻¹ ·G)⁻¹ ·G ^(T) ·Q _(dd) ⁻¹  (15)Vector of residuals is then(Y−N)−G·{circumflex over (x)}=(y−N)−G·G ^(L)(y−N)=(I−G·G^(L))(y−N)=S(y−N)  (16)which is a function of N and local minima search tries to minimizeweighted norm square of residuals with respect to N asmin c(N)=(y−N)^(T) ·W·(y−N), where W=S ^(T) ·Q _(dd) ⁻¹ ·S and S=I−G·G^(T)  (17)To solve (17) consider solvingW·N≈W·y  (18)under the constraint that N is integer. Then W·(y−N)≈0 and(y−N)^(T)·W^(T)·W·(y−N)=(y−N)^(T)·W·(y−N)=c(N)≈0 because W is idempotent(W^(T)=W and W·W=W). Thus search for N is limited to those N whichsatisfy (18).

Once N is solved for estimate of x=Δp_(u) is obtained from equation(15).

Matrices G and G^(L), of dimensions (n−1)×3 and 3×(n−1) respectivelyhave rank 3 each since (n−1)>3 and so (n−1)×(n−1) matrices S and W willfall short from full rank of (n−1) by 3.

Using QR decomposition of W (LU decomposition could also be used) onequation (18),R·N=Q ^(T) ·W·y  (19)where Q is ortho-normal matrix (Q⁻¹=Q^(T)) and R is upper triangular sothat

$\begin{matrix}{{\begin{bmatrix}R_{11} & R_{12} \\0 & 0\end{bmatrix} \cdot \begin{bmatrix}N_{1} \\N_{2}\end{bmatrix}} = \begin{bmatrix}\left( {Q^{T} \cdot W \cdot y} \right)_{11} \\{\approx 0}\end{bmatrix}} & (20)\end{matrix}$and thenN ₁=round{R ₁₁ ⁻¹·((Q ^(T) ·W·y)₁₁ −R ₁₂ ·N ₂)}  (21)

Thus solution of

$N = \begin{bmatrix}N_{1} \\N_{2}\end{bmatrix}$is obtained by searching for N₂ in 3 dimensional box with integervalues, obtaining N₁ from (21), and picking that N which minimizes c(N)in (17). Search for N₂ is centered on the value of N₂ from the previousiteration. At the zero-th iteration N₂ latter part of N which isobtained as fractional part of λ⁻¹·ƒ(p_(u) ⁰); p_(u) ⁰ being the codephase based solution. The size of the 3 dimensional search box dependson the uncertainty in the code phase based solution. This box can bedivided into smaller sub-boxes and center of each smaller size sub-boxcan be tried as initial p_(u) ⁰.

The above method used a single epoch (instant) of measurement todetermine position. The description below explains an extension to thesingle epoch method. Multiple epoch measurements are taken close enoughin time wherein user receiver movement is negligible. Further, integerambiguities of the initial epoch remain the same for subsequent epochsso that no new unknown integer ambiguities are introduced at subsequentepochs. Multiple epoch measurements do not give independent equationsbecause transmitter locations are fixed (unlike in the GNSS case wheremotion of satellite transmitters change line-of-sight and thus giveindependent equations). So multiple epoch measurements do not help insolving for integer ambiguities as float ambiguities (unlike in GNSScase when number of independent equations become greater than number ofunknown ambiguities plus three position coordinates). However, multipleepoch measurements allow more carrier phase measurement errors and stillallow successful ambiguity resolution. In the multiple epoch caseequation (13) becomes

$\begin{matrix}{y = {\begin{bmatrix}y_{1} \\y_{2} \\\vdots \\y_{m}\end{bmatrix} = {{\begin{bmatrix}G \\G \\\vdots \\G\end{bmatrix} \cdot x} + \begin{bmatrix}N \\N \\\vdots \\N\end{bmatrix} + \begin{bmatrix}ɛ_{1} \\ɛ_{2} \\\vdots \\ɛ_{m}\end{bmatrix}}}} & (22)\end{matrix}$Following development for single epoch case as above equation, theproblem reduces to problem of finding N such that

$\begin{matrix}{{{\min\;{c(N)}} = {\left( {y - \begin{bmatrix}N \\N \\\vdots \\N\end{bmatrix}} \right)^{T} \cdot \overset{\_}{W} \cdot \left( {y - \begin{bmatrix}N \\N \\\vdots \\N\end{bmatrix}} \right)}},} & (23)\end{matrix}$where W=S ^(T)·Q _(dd) ⁻¹·S, S=I−G·G ^(L), G ^(L)=(G ^(T)·Q_(dd−1)·G)⁻¹·G ^(T)·Q _(dd) ⁻¹

$\overset{\_}{G} = \begin{bmatrix}G \\G \\\vdots \\G\end{bmatrix}$ ${\overset{\_}{Q}}_{dd}^{- 1} = \begin{bmatrix}Q_{dd}^{- 1} & 0 & \ldots & 0 \\0 & Q_{dd}^{- 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & Q_{dd}^{- 1}\end{bmatrix}$And to solve (23) for N consider solving

$\begin{matrix}{{{\overset{\_}{W} \cdot \overset{\_}{I} \cdot N} \approx {{\overset{\_}{W} \cdot y}\mspace{14mu}{where}\mspace{14mu}\overset{\_}{I}}} = \begin{bmatrix}I \\I \\\vdots \\I\end{bmatrix}} & (24)\end{matrix}$using QR decomposition of W·Ī (LU decomposition could also be used) andfollowing equations of (19) to (21) as above. Again, once N is solvedfor estimate of x=Δp_(u) is obtained from equation (15). If thisestimate of x=Δp_(u) is small then iterations in equation (11) arestopped to obtain user position p_(u). Typically if each component of xis less than 1e-6 in magnitude then convergence is declared anditerations are stopped.

The next step is to verify whether the converged user position p_(u) isthe right one. This is done based on residuals obtained from (10) asmod(ϕ−λ⁻¹·ƒ(p_(u))−N,λ). If maximum of absolute values of residuals foreach epoch is less than κ·√{square root over (Q_(r))} then convergedsolution is accepted as a solution otherwise the search is continued byselecting a new sub-box. Typically scale factor κ in the verificationtest can be chosen to be 5. Once the solution is verified, thedifferential WAPS system described above can achieve accuracy close toor better than 1 m.

This differential WAPS carrier phase system may be overlaid on top ofthe traditional WAPS system through the addition of reference receiversor can be standalone. The differential WAPS carrier phase system can beused to deliver high accuracy positioning in certain localized targetareas (such as malls, warehouses etc.).

In W-CDMA systems, two receive chains are used to improve the receivediversity. When WAPS co-exists with W-CDMA, one of the receive chainscan be used temporarily for receiving and processing the WAPS signal. Incertain cases of W-CDMA and CDMA architectures, the entire receive chaincan be reused to receive WAPS signal by tuning the receiver to WAPS bandand processing the WAPS signal while temporarily suspending theprocessing of the W-CDMA/CDMA signals. In certain other embodimentswhere the GSM receive chain is multiplexed with the W-CDMA receivechain, the receiver can be further time-shared to be used for WAPSreception.

Once it is determined which signals are used from which towers forposition determination in WAPS or any other TDMA system, in order tosave power, most of the receiver of an embodiment is turned off duringthe slots at which either signal is not detected and/or signals fromtowers that radiate in those slots are not used for positiondetermination. In case of detection of motion or change in position orchange in signal conditions, then the receiver of an embodiment isturned ON for all the slots to determine which slots can be used fornext set of position calculations.

Embodiments described herein include a position location systemcomprising a transmitter network including a plurality of transmittersthat broadcast a plurality of positioning signals. Each positioningsignal of the plurality of positioning signals comprises a pseudorandomranging signal. The system includes a remote receiver that acquires andmeasures the time of arrival of the plurality of positioning signalsreceived at the remote receiver. During an interval of time at least twopositioning signals are transmitted concurrently, each by a differentmember of the plurality of transmitters, and received concurrently atthe remote receiver. The at least two positioning signals have differentcarrier frequencies. The different carrier frequencies are offset fromone another by an amount that is at least one of less than and equal totwenty-five percent of the bandwidth of each positioning signal of theat least two positioning signals.

Embodiments described herein include a position location systemcomprising: a transmitter network comprising a plurality of transmittersthat broadcast a plurality of positioning signals, wherein eachpositioning signal of the plurality of positioning signals comprises apseudorandom ranging signal; and a remote receiver that acquires andmeasures the time of arrival of the plurality of positioning signalsreceived at the remote receiver; wherein during an interval of time atleast two positioning signals are transmitted concurrently, each by adifferent member of the plurality of transmitters, and receivedconcurrently at the remote receiver, wherein the at least twopositioning signals have different carrier frequencies, the differentcarrier frequencies offset from one another by an amount that is atleast one of less than and equal to twenty-five percent of the bandwidthof each positioning signal of the at least two positioning signals.

The offset of an embodiment is a multiple of a sum of a frame rate ofthe pseudorandom ranging signals and a fraction 1/n of the frame rate,where n is an integer.

The at least two positioning signals of an embodiment have differentpseudorandom codes.

The at least two positioning signals of an embodiment have the samepseudorandom codes.

The pseudorandom ranging signal of an embodiment is repeated a pluralityof times in succession.

During the interval of time of an embodiment at least two additionalpositioning signals are transmitted non-concurrently by the plurality oftransmitters.

The at least two additional positioning signals of an embodiment have asame pseudorandom code.

The plurality of transmitters of an embodiment is arranged in ageometric pattern and uses a plurality of time slots to broadcast theplurality of positioning signals.

The plurality of transmitters of an embodiment comprises at least mtransmitters using n time slots in a time multiplexing frame tobroadcast the plurality of positioning signals, where m and n arepositive integers.

The variable m of an embodiment is greater than n.

The variable m of an embodiment is at least one of less than and equalto n.

At least one of the at least m transmitters of an embodiment transmitsin more than one slot in a time multiplexing frame.

Each of the at least m transmitters of an embodiment use a pseudorandomcode selected among a set of k pseudorandom codes to transmit theirpseudorandom ranging signal, wherein k is a number greater than 1.

The variable k of an embodiment is at least one of greater than andequal to n.

At least one transmitter of the plurality of transmitters of anembodiment transmits a positioning signal in at least two successivetime multiplexing frames of a positioning signal.

The at least two successive time multiplexing frames of an embodimentcomprise a primary frame and a secondary frame, wherein positioning datais transmitted in the primary frame.

Auxiliary data of an embodiment is transmitted in the secondary frame,where the auxiliary data comprises at least one of security data andauthentication data.

Positioning data of an embodiment is transmitted in the secondary frame.

The at least two positioning signals of an embodiment are transmittedconcurrently by at least two transmitters in a vicinity of one another,wherein the at least two positioning signals have at least one commonparameter.

The at least one common parameter of an embodiment is at least one of apseudorandom code, and positioning signal data.

The pseudorandom code of an embodiment is a maximal length pseudorandomcode.

The pseudorandom code of an embodiment is a Gold Code.

The plurality of transmitters of an embodiment comprises a supergroup oftransmitters, wherein the supergroup includes a plurality of groups oftransmitters arranged in a geometric pattern, and each group includes aplurality of transmitters arranged in a geometric pattern.

The plurality of groups of a supergroup of an embodiment comprises ann-group repeat pattern, wherein n is an integer.

The geometric pattern of the supergroup of an embodiment comprises ahexagonal pattern of groups.

The plurality of groups of a supergroup of an embodiment comprises seven(7) groups.

Each group of an embodiment comprises seven (7) transmitters.

The supergroup of an embodiment comprises at least one of a timedivision multiplexing (TDMA) communication network, a code divisionmultiplexing (CDMA) communication network, and a frequency offsetmultiplexing (FOM) network.

The at least two positioning signals of an embodiment are transmittedconcurrently by at least two transmitters of a group of the plurality ofgroups.

The at least two positioning signals of an embodiment are transmittedconcurrently by at least two transmitters that are in different groups.

The plurality of positioning signals of an embodiment comprises a set ofpseudorandom codes, wherein each group in the plurality of groups oftransmitters utilizes a permutation of the set of pseudorandom codes.

The permutation of the set of pseudorandom codes of an embodiment iscyclic with respect to a slot number of the transmitter.

The permutation of an embodiment associates each pseudorandom code inthe set to a geographical position of each transmitter in a group.

A position of a transmitter in each group of an embodiment is associatedwith a transmit time slot.

Each group of the plurality of groups of an embodiment uses a pluralityof time slots to broadcast the plurality of positioning signals.

Each group of the plurality of groups of an embodiment comprises ntransmitters using n time slots to broadcast the plurality ofpositioning signals, where n is an integer.

Each group of the plurality of groups of an embodiment uses a same setof time slots to broadcast the plurality of positioning signals.

Each transmitter of a group of an embodiment broadcasts in a differenttime slot from any other transmitter of the group.

Each group of the plurality of groups of a supergroup of an embodimentuses at least one pseudorandom code that is different from thepseudorandom code of any other group.

The at least one pseudorandom code of an embodiment comprises a GoldCode.

Each group of the plurality of groups of the supergroup of an embodimentuses an offset in frequency that is different than the offset of anyother group.

Each group of the plurality of groups of the supergroup of an embodimentuses an offset in frequency that is different than the offset of fromany other group.

The plurality of transmitters of the plurality of groups of a supergroupof an embodiment uses a common pseudorandom code for a least a portionof their transmissions.

The pseudorandom code of an embodiment comprises a Gold Code.

The pseudorandom code of an embodiment comprises a maximal lengthpseudorandom sequence.

The maximal length pseudorandom sequence of an embodiment comprises afirst of two maximal length sequences forming a Gold Code.

Each transmitter of a group of an embodiment broadcasts using adifferent pseudorandom code from any other transmitter of the group.

Each group of the plurality of groups of a supergroup of an embodimentuses a set of pseudorandom codes that is the same as every other groupof the plurality of groups.

Each group of the plurality of groups of the supergroup of an embodimentuses an offset in frequency that is different than the offset from anyother group.

Each transmitter of the supergroup of an embodiment broadcasts using adifferent pseudorandom code from any other transmitter of thesupergroup.

Each group of the plurality of groups of the supergroup of an embodimentuses an offset in frequency that is different than the offset of fromany other group.

Each group of the plurality of groups of a supergroup of an embodimentuses at least one pseudorandom code in accordance with a maximal lengthpseudorandom sequence.

The at least one pseudorandom code of each group of the supergroup of anembodiment is different from the pseudorandom code of any other group ofthe supergroup.

Each group of the plurality of groups of the supergroup of an embodimentuses an offset in frequency that is different than the offset of anyother group of the supergroup.

Each group of the plurality of groups of the supergroup of an embodimentuses an offset in frequency that is different than the offset of fromany other group.

Each group of the supergroup of an embodiment uses a pseudorandom codedifferent from that of a pseudorandom code used by any other group ofthe supergroup.

Each group of the plurality of groups of a supergroup of an embodimentuses a same set of pseudorandom codes, wherein the pseudorandom codes ofeach group are permuted relative to slot numbers of every other group ofthe plurality of groups.

Each group of the plurality of groups of the supergroup of an embodimentuses an offset in frequency that is different than the offset of fromany other group.

The plurality of transmitters of an embodiment comprises a plurality ofsupergroups of transmitters, wherein each supergroup of the plurality ofsupergroups comprises a plurality of groups of transmitters arranged ina geometric pattern.

Each transmitter of a group of an embodiment broadcasts using adifferent pseudorandom code from any other transmitter of the group.

Each supergroup of the plurality of supergroups of an embodiment uses asame set of pseudorandom codes as every other supergroup of theplurality of supergroups, wherein the pseudorandom codes of eachsupergroup are permuted relative to slot numbers of every othersupergroup of the plurality of supergroups.

Each group of the plurality of groups of a supergroup of an embodimentuses an offset in frequency that is different than the offset infrequency of any other group of that same supergroup.

In each supergroup of the plurality of supergroups of an embodiment,each transmitter broadcasts using a different pseudorandom code from anyother transmitter of that same supergroup.

Each supergroup of an embodiment uses a same set of pseudorandom codesas used by every other supergroup, wherein the pseudorandom codes of asupergroup are permuted relative to slot numbers of every othersupergroup.

A measure of performance corresponding to the geometric pattern of anembodiment is a ratio of distance between transmitters using identicaltransmission parameters and a transmitter radius.

A measure of performance corresponding to the geometric pattern of anembodiment is correlation rejection associated with the multiplexingprotocol used by the supergroup.

Each carrier frequency of an embodiment is the sum of a base frequencyplus an element of a set of offsets, and each offset in the set ofoffsets is a multiple of a minimum nonzero offset.

The set of offsets of an embodiment corresponds to0,k ₀ R+R/Q,2k ₀ R+2R/Q,3k ₀ R+3R/Q . . . ,(Q−1)k ₀ R+(Q−1)R/Q,where R represents PN frame rate, k₀ represents a nonzero integer, and Qrepresents an integer equal to a number of offsets.

The integer k₀ of an embodiment has magnitude that is at least one ofequal to and greater than two (2).

Quantity Q of an embodiment equals a number of PN frames of thepositioning signal coherently integrated by said remote receiver.

The number of PN frames of the positioning signal coherently integratedby the remote receiver of an embodiment is equal to an integer multipleof Q.

The quantity Q of an embodiment equals the number of groups oftransmitters in the supergroup, and a number of PN frames of thepositioning signal coherently integrated by said receiver is greaterthan the number of groups of transmitters in the supergroup.

The position location system of an embodiment comprises a set of carrierfrequency offsets from a base frequency, wherein each offset in the setis at least one of equal to and less than twenty-five percent of thebandwidth of each of the plurality of positioning signals.

Embodiments described herein include a position location systemcomprising a transmitter network including a plurality of transmittersthat broadcast a plurality of positioning signals comprising rangingdata. The system includes a remote receiver that acquires and measuresthe time of arrival of the plurality of positioning signals received atthe remote receiver. During an interval of time at least two positioningsignals are transmitted concurrently, each by a different member of theplurality of transmitters, and received concurrently at the remotereceiver. The at least two positioning signals have different carrierfrequencies. The carrier frequencies are offset from one another by anamount that is less than 50% of an instantaneous bandwidth of eachpositioning signal of the at least two positioning signals.

Embodiments described herein include a position location systemcomprising: a transmitter network comprising a plurality of transmittersthat broadcast a plurality of positioning signals comprising rangingdata; and a remote receiver that acquires and measures the time ofarrival of the plurality of positioning signals received at the remotereceiver; wherein during an interval of time at least two positioningsignals are transmitted concurrently, each by a different member of theplurality of transmitters, and received concurrently at the remotereceiver, wherein the at least two positioning signals have differentcarrier frequencies, the carrier frequencies offset from one another byan amount that is less than 50% of an instantaneous bandwidth of eachpositioning signal of the at least two positioning signals.

The remote receiver of an embodiment tunes to a frequency of a selectedpositioning signal of the at least two positioning signals, andcorrelates the selected positioning signal with a reference pseudorandomranging signal matched to a transmitted pseudorandom ranging signal ofthe selected positioning signal, wherein the correlation reduces thecross-interference to the selected positioning signal produced bynonselected signals.

Embodiments described herein include a transmitter in a positionlocation system comprising a plurality of transmitters broadcasting aplurality of positioning signals. The plurality of positioning signalsincludes wideband pseudorandom ranging signals. The transmittercomprises a processor coupled to a memory and running at least oneapplication that selects a first frequency from a sum of a basefrequency plus a first offset that belongs to a set of offsets. Theapplication generates a first positioning signal comprising a carrier atthe first frequency. The application transmits the first positioningsignal concurrently with transmission of a second positioning signalfrom a second transmitter of the plurality of transmitters. The secondpositioning signal has a carrier at a second frequency that is the sumof the base frequency plus a second offset belonging to the set ofoffsets. The first and second offsets are different by an amount that isat least one of equal to and less than 25 percent of the bandwidth ofeach of the plurality of positioning signals.

Embodiments described herein include a transmitter in a positionlocation system comprising a plurality of transmitters broadcasting aplurality of positioning signals, wherein the plurality of positioningsignals includes wideband pseudorandom ranging signals, the transmittercomprising: a processor coupled to a memory and running at least oneapplication that, selects a first frequency from a sum of a basefrequency plus a first offset that belongs to a set of offsets;generates a first positioning signal comprising a carrier at the firstfrequency; and transmits the first positioning signal concurrently withtransmission of a second positioning signal from a second transmitter ofthe plurality of transmitters, wherein the second positioning signal hasa carrier at a second frequency that is the sum of the base frequencyplus a second offset belonging to the set of offsets, and wherein thefirst and second offsets are different by an amount that is at least oneof equal to and less than 25 percent of the bandwidth of each of theplurality of positioning signals.

The first positioning signal and the second positioning signal of anembodiment comprise different pseudorandom codes.

The first positioning signal and the second positioning signal of anembodiment comprise the same pseudorandom codes.

The wideband pseudorandom ranging signals of an embodiment are repeateda plurality of times in succession.

The at least one application of an embodiment transmits a positioningsignal in at least two successive time multiplexing frames of the firstpositioning signal.

The at least two successive time multiplexing frames of an embodimentcomprise a primary frame and a secondary frame, wherein positioning datais transmitted in the primary frame.

Auxiliary data of an embodiment is transmitted in the secondary frame,where the auxiliary data comprises at least one of security data andauthentication data.

Positioning data of an embodiment is transmitted in the secondary frame.

The second transmitter of an embodiment is in a vicinity of thetransmitter and the first positioning signal and the second positioningsignal have at least one common parameter.

The at least one common parameter of an embodiment is at least one of apseudorandom code, and positioning signal data.

The pseudorandom code of an embodiment is a maximal length pseudorandomcode.

The maximal length pseudorandom code of an embodiment comprises a firstof two maximal length sequences forming a Gold Code.

The pseudorandom code of an embodiment is a Gold Code.

The transmitter and the second transmitter of an embodiment belong to asame group of transmitters geographically adjacent to one another.

The transmitter and the second transmitter of an embodiment belong todifferent groups of transmitters, wherein each of the different groupshave transmitters that are geographically adjacent to one another.

The set of offsets of an embodiment comprises offsets that are each amultiple of a sum of a frame rate of the wideband pseudorandom rangingsignals and a fraction 1/n of the frame rate, where n is an integer.

Each offset of the set of offsets of an embodiment is a multiple of aminimum nonzero offset.

The set of offsets of an embodiment corresponds to0,k ₀ R+R/Q,2k ₀ R+2R/Q,3k ₀ R+3R/Q . . . ,(Q−1)k ₀ R+(Q−1)R/Q,where R represents PN frame rate, k₀ represents a nonzero integer, and Qrepresents an integer equal to the number of offsets.

The integer k₀ of an embodiment has magnitude that is at least one ofequal to and greater than two (2).

Quantity Q of an embodiment equals a number of PN frames of thepositioning signal coherently integrated by said remote receiver.

Cross-interference of the second positioning signal upon the firstpositioning signal of an embodiment is reduced at a remote receiver bytuning the remote receiver to a frequency of the first positioningsignal and correlating the signal received by the receiver with areference pseudorandom ranging signal matched to a transmittedpseudorandom ranging signal of the first positioning signal.

Embodiments described herein include a receiver in a position locationsystem. The receiver comprises a processor coupled to a memory andrunning at least one application that receives during an interval oftime at least two positioning signals, each transmitted concurrently bydifferent transmitters of a plurality of transmitters. The at least twopositioning signals comprise wideband pseudorandom ranging signalshaving carrier frequencies different from each other. The carrierfrequencies are offset from one another by an amount that is at leastone of equal to and less than twenty-five percent of a bandwidth of eachpositioning signal of the at least two positioning signals. Theapplication tunes to a frequency of a selected positioning signal of theat least two positioning signals. The application correlates theselected positioning signal with a reference pseudorandom ranging signalmatched to a transmitted pseudorandom ranging signal of the selectedpositioning signal. The correlation reduces the cross-interference tothe selected positioning signal produced by nonselected signals.

Embodiments described herein include a receiver in a position locationsystem, the receiver comprising: a processor coupled to a memory andrunning at least one application that, receives during an interval oftime at least two positioning signals, each transmitted concurrently bydifferent transmitters of a plurality of transmitters, the at least twopositioning signals comprising wideband pseudorandom ranging signalshaving carrier frequencies different from each other, the carrierfrequencies offset from one another by an amount that is at least one ofequal to and less than twenty-five percent of a bandwidth of eachpositioning signal of the at least two positioning signals; tunes to afrequency of a selected positioning signal of the at least twopositioning signals; and correlates the selected positioning signal witha reference pseudorandom ranging signal matched to a transmittedpseudorandom ranging signal of the selected positioning signal, whereinthe correlation reduces the cross-interference to the selectedpositioning signal produced by nonselected signals.

The offset of an embodiment is a multiple of a sum of a frame rate ofthe wideband pseudorandom ranging signals and a fraction 1/n of theframe rate, where n is an integer.

The at least two positioning signals of an embodiment comprise differentpseudorandom codes.

The at least two positioning signals of an embodiment comprise the samepseudorandom codes.

The wideband pseudorandom ranging signals of an embodiment are repeateda plurality of times in succession.

During the interval of time of an embodiment at least two additionalpositioning signals are received, wherein the at least two additionalpositioning signals are transmitted non-concurrently by the plurality oftransmitters.

The at least two additional positioning signals of an embodimentcomprise a same pseudorandom code.

A plurality of time slots of an embodiment are used to broadcast aplurality of positioning signals comprising the at least two positioningsignals.

Each of the at least two positioning signals of an embodiment comprise apositioning signal transmitted in at least two successive timemultiplexing frames of a positioning signal.

The at least two successive time multiplexing frames of an embodimentcomprise a primary frame and a secondary frame, wherein positioning datais transmitted in the primary frame.

Auxiliary data of an embodiment is transmitted in the secondary frame,where the auxiliary data comprises at least one of security data andauthentication data.

Positioning data of an embodiment is transmitted in the secondary frame.

The at least two positioning signals of an embodiment are transmittedconcurrently by at least two transmitters in a vicinity of one another,wherein the at least two positioning signals have at least one commonparameter.

The at least one common parameter of an embodiment is at least one of apseudorandom code, and positioning signal data.

The pseudorandom code of an embodiment is a maximal length pseudorandomcode.

The maximal length pseudorandom code of an embodiment comprises a firstof two maximal length sequences forming a Gold Code.

The pseudorandom code of an embodiment is a Gold Code.

Each carrier frequency of an embodiment is the sum of a base frequencyplus an element of a set of offsets, and each offset is a multiple of aminimum nonzero offset.

The set of offsets of an embodiment corresponds to0,k ₀ R+R/Q,2k ₀ R+2R/Q,3k ₀ R+3R/Q . . . ,(Q−1)k ₀ R+(Q−1)R/Q,where R represents PN frame rate, k₀ represents a nonzero integer, and Qrepresents an integer equal to a number of offsets.

The integer k₀ of an embodiment has magnitude that is at least one ofequal to and greater than two (2).

Quantity Q of an embodiment equals a number of PN frames of thepositioning signal coherently integrated by said remote receiver.

The at least one application of an embodiment coherently integrates anumber of PN frames of a received positioning signal, wherein the numberof PN frames is equal to an integer multiple of Q.

Embodiments described herein include a method of reducingcross-interference in a position location system. The method comprisesbroadcasting from a plurality of transmitters of a transmitter network aplurality of positioning signals comprising pseudorandom rangingsignals. During an interval of time at least two positioning signals aretransmitted concurrently, each by a different member of the plurality oftransmitters. The at least two positioning signals comprise a firstsignal transmitted from a first member and a second signal transmittedfrom a second member. The at least two positioning signals havedifferent carrier frequencies. The carrier frequencies are offset fromone another by an amount that is at least one of equal to and less thantwenty-five percent of the bandwidth of each positioning signal of theat least two positioning signals. The method receives in a remotereceiver the at least two positioning signals. The method reduces thecross-interference of the second signal upon the first by tuning theremote receiver to a frequency of the first signal and correlating thereceived signal with a reference pseudorandom ranging signal matched toa transmitted pseudorandom ranging signal of the first signal.

Embodiments described herein include a method of reducingcross-interference in a position location system, the method comprising:broadcasting from a plurality of transmitters of a transmitter network aplurality of positioning signals comprising pseudorandom rangingsignals, wherein during an interval of time at least two positioningsignals are transmitted concurrently, each by a different member of theplurality of transmitters, wherein the at least two positioning signalscomprise a first signal transmitted from a first member and a secondsignal transmitted from a second member, wherein the at least twopositioning signals have different carrier frequencies, the carrierfrequencies offset from one another by an amount that is at least one ofequal to and less than twenty-five percent of the bandwidth of eachpositioning signal of the at least two positioning signals; receiving ina remote receiver the at least two positioning signals; and reducing thecross-interference of the second signal upon the first by tuning theremote receiver to a frequency of the first signal and correlating thereceived signal with a reference pseudorandom ranging signal matched toa transmitted pseudorandom ranging signal of the first signal.

The offset of an embodiment is a multiple of a sum of a frame rate ofthe pseudorandom ranging signals and a fraction 1/n of the frame rate,where n is an integer.

The method of an embodiment comprises generating the at least twopositioning signals to have different pseudorandom codes.

The method of an embodiment comprises generating the at least twopositioning signals to have the same pseudorandom codes.

The method of an embodiment comprises repeating the pseudorandom rangingsignals a plurality of times in succession.

The method of an embodiment comprises non-concurrently transmitting bythe plurality of transmitters at least two additional positioningsignals.

The method of an embodiment comprises generating the at least twoadditional positioning signals to have a same pseudorandom code.

The method of an embodiment comprises arranging the plurality oftransmitters in a geometric pattern and using a plurality of time slotsto broadcast the plurality of positioning signals.

The plurality of transmitters of an embodiment comprises at least mtransmitters using n time slots in a time multiplexing frame tobroadcast the plurality of positioning signals, where m and n arepositive integers.

The variable m of an embodiment is greater than n.

The variable m of an embodiment is at least one of less than and equalto n.

The method of an embodiment comprises at least one of the at least mtransmitters transmitting in more than one slot in a time multiplexingframe.

The method of an embodiment comprises transmitting the pseudorandomranging signal from each of the at least m transmitters using apseudorandom code selected among a set of k pseudorandom codes, whereink is a number greater than 1.

The variable k of an embodiment is at least one of greater than andequal to n.

The method of an embodiment comprises transmitting from at least onetransmitter of the plurality of transmitters a positioning signal in atleast two successive time multiplexing frames of a positioning signal.

The at least two successive time multiplexing frames of an embodimentcomprise a primary frame and a secondary frame, wherein positioning datais transmitted in the primary frame.

The method of an embodiment comprises transmitting auxiliary data in thesecondary frame, where the auxiliary data comprises at least one ofsecurity data and authentication data.

The method of an embodiment comprises transmitting positioning data inthe secondary frame.

The method of an embodiment comprises transmitting the at least twopositioning signals concurrently by at least two transmitters in avicinity of one another, wherein the at least two positioning signalshave at least one common parameter.

The at least one common parameter of an embodiment is at least one of apseudorandom code, and positioning signal data.

The pseudorandom code of an embodiment is a maximal length pseudorandomcode.

The pseudorandom code of an embodiment is a Gold Code.

The plurality of transmitters of an embodiment comprises a supergroup oftransmitters, wherein the supergroup includes a plurality of groups oftransmitters arranged in a geometric pattern, and each group includes aplurality of transmitters arranged in a geometric pattern.

The plurality of groups of a supergroup of an embodiment comprises ann-group repeat pattern, wherein n is an integer.

The geometric pattern of the supergroup of an embodiment comprises ahexagonal pattern of groups.

The plurality of groups of a supergroup of an embodiment comprises seven(7) groups.

Each group of an embodiment comprises seven (7) transmitters.

The supergroup of an embodiment comprises at least one of a timedivision multiplexing

(TDMA) communication network, a code division multiplexing (CDMA)communication network, and a frequency offset multiplexing (FOM)network.

The method of an embodiment comprises transmitting the at least twopositioning signals concurrently by at least two transmitters of a groupof the plurality of groups.

The method of an embodiment comprises transmitting the at least twopositioning signals concurrently by at least two transmitters that arein different groups.

The plurality of positioning signals of an embodiment comprises a set ofpseudorandom codes, wherein each group in the plurality of groups oftransmitters utilizes a permutation of the set of pseudorandom codes.

The permutation of the set of pseudorandom codes of an embodiment iscyclic with respect to a slot number of the transmitter.

The permutation of an embodiment associates each pseudorandom code inthe set to a geographical position of each transmitter in a group.

The method of an embodiment comprises associating a position of atransmitter in each group with a transmit time slot.

The method of an embodiment comprises each group of the plurality ofgroups using a plurality of time slots to broadcast the plurality ofpositioning signals.

Each group of the plurality of groups of an embodiment comprises ntransmitters using n time slots to broadcast the plurality ofpositioning signals, where n is an integer.

The method of an embodiment comprises each group of the plurality ofgroups using a same set of time slots to broadcast the plurality ofpositioning signals.

The method of an embodiment comprises each transmitter of a groupbroadcasting in a different time slot from any other transmitter of thegroup.

The method of an embodiment comprises each group of the plurality ofgroups of a supergroup using at least one pseudorandom code that isdifferent from the pseudorandom codes of any other group.

The at least one pseudorandom code of an embodiment comprises a GoldCode.

The method of an embodiment comprises each group of the plurality ofgroups of the supergroup using an offset in frequency that is differentthan the offset of any other group.

The method of an embodiment comprises each group of the plurality ofgroups of the supergroup using an offset in frequency that is differentthan the offset of from any other group.

The method of an embodiment comprises the plurality of transmitters ofthe plurality of groups of a supergroup using a common pseudorandom codefor a least a portion of their transmissions.

The pseudorandom code of an embodiment comprises a Gold Code.

The pseudorandom code of an embodiment comprises a maximal lengthpseudorandom sequence.

The maximal length pseudorandom sequence of an embodiment comprises afirst of two maximal length sequences forming a Gold Code.

The method of an embodiment comprises each transmitter of a groupbroadcasts using a different pseudorandom code from any othertransmitter of the group.

The method of an embodiment comprises each group of the plurality ofgroups of a supergroup using a set of pseudorandom codes that is thesame as every other group of the plurality of groups.

The method of an embodiment comprises each group of the plurality ofgroups of the supergroup using an offset in frequency that is differentthan the offset from any other group.

The method of an embodiment comprises each transmitter of the supergroupbroadcasting using a different pseudorandom code from any othertransmitter of the supergroup.

The method of an embodiment comprises each group of the plurality ofgroups of the supergroup using an offset in frequency that is differentthan the offset of from any other group.

The method of an embodiment comprises each group of the plurality ofgroups of a supergroup using at least one pseudorandom code inaccordance with a maximal length pseudorandom sequence.

The at least one pseudorandom code of each group of the supergroup of anembodiment is different from the pseudorandom codes of any other groupof the supergroup.

The method of an embodiment comprises each group of the plurality ofgroups of the supergroup using an offset in frequency that is differentthan the offset of any other group of the supergroup.

The method of an embodiment comprises each group of the plurality ofgroups of the supergroup using an offset in frequency that is differentthan the offset of from any other group.

The method of an embodiment comprises each group of the supergroup usinga pseudorandom code different from that of a pseudorandom code used byany other group of the supergroup.

The method of an embodiment comprises each group of the plurality ofgroups of a supergroup using a same set of pseudorandom codes, andpermuting the pseudorandom codes of each group relative to slot numbersof every other group of the plurality of groups.

The method of an embodiment comprises each group of the plurality ofgroups of the supergroup using an offset in frequency that is differentthan the offset of from any other group.

The plurality of transmitters of an embodiment comprises a plurality ofsupergroups of transmitters, wherein each supergroup of the plurality ofsupergroups comprises a plurality of groups of transmitters arranged ina geometric pattern.

The method of an embodiment comprises each transmitter of a groupbroadcasting using a different pseudorandom code from any othertransmitter of the group.

The method of an embodiment comprises each supergroup of the pluralityof supergroups using a same set of pseudorandom codes as every othersupergroup of the plurality of supergroups, and permuting thepseudorandom codes of each supergroup relative to slot numbers of everyother supergroup of the plurality of supergroups.

The method of an embodiment comprises each group of the plurality ofgroups of a supergroup using an offset in frequency that is differentthan the offset in frequency of any other group of that same supergroup

The method of an embodiment comprises, in each supergroup of theplurality of supergroups, each transmitter broadcasting using adifferent pseudorandom code from any other transmitter of that samesupergroup.

The method of an embodiment comprises each supergroup using a same setof pseudorandom codes as used by every other supergroup, and permutingthe pseudorandom codes of a supergroup relative to slot numbers of everyother supergroup.

The method of an embodiment comprises measuring performancecorresponding to the geometric pattern using a ratio of distance betweentransmitters having identical transmission parameters and a transmitterradius.

The method of an embodiment comprises measuring performancecorresponding to the geometric pattern using correlation rejectionassociated with the multiplexing protocol used by the supergroup.

The method of an embodiment comprises generating each carrier frequencyas a sum of a base frequency plus an element of a set of offsets,wherein each offset in the set of offsets is a multiple of a minimumnonzero offset.

The set of offsets of an embodiment corresponds to0,k ₀ R+R/Q,2k ₀ R+2R/Q,3k ₀ R+3R/Q . . . ,(Q−1)k ₀ R+(Q−1)R/Q,where R represents PN frame rate, k₀ represents a nonzero integer, and Qrepresents an integer equal to a number of offsets.

The integer k₀ of an embodiment has magnitude that is at least one ofequal to and greater than two (2).

Quantity Q of an embodiment equals a number of PN frames of thepositioning signal coherently integrated by said remote receiver.

The number of PN frames of the positioning signal coherently integratedby the remote receiver of an embodiment is equal to an integer multipleof Q.

The quantity Q of an embodiment equals the number of groups oftransmitters in the supergroup, and a number of PN frames of thepositioning signal coherently integrated by said receiver is greaterthan the number of groups of transmitters in the supergroup.

The method of an embodiment comprises a set of carrier frequency offsetsfrom a base frequency, wherein each offset in such set is no greaterthan twenty-five percent of the bandwidth of each of the plurality ofpositioning signals.

The components described herein can be located together or in separatelocations. Communication paths couple the components and include anymedium for communicating or transferring files among the components. Thecommunication paths include wireless connections, wired connections, andhybrid wireless/wired connections. The communication paths also includecouplings or connections to networks including local area networks(LANs), metropolitan area networks (MANs), wide area networks (WANs),proprietary networks, interoffice or backend networks, and the Internet.Furthermore, the communication paths include removable fixed mediumslike floppy disks, hard disk drives, and CD-ROM disks, as well as flashRAM, Universal Serial Bus (USB) connections, RS-232 connections,telephone lines, buses, and electronic mail messages.

Aspects of the systems and methods described herein may be implementedas functionality programmed into any of a variety of circuitry,including programmable logic devices (PLDs), such as field programmablegate arrays (FPGAs), programmable array logic (PAL) devices,electrically programmable logic and memory devices and standardcell-based devices, as well as application specific integrated circuits(ASICs). Some other possibilities for implementing aspects of thesystems and methods include: microcontrollers with memory (such aselectronically erasable programmable read only memory (EEPROM)),embedded microprocessors, firmware, software, etc. Furthermore, aspectsof the systems and methods may be embodied in microprocessors havingsoftware-based circuit emulation, discrete logic (sequential andcombinatorial), custom devices, fuzzy (neural) logic, quantum devices,and hybrids of any of the above device types. Of course the underlyingdevice technologies may be provided in a variety of component types,e.g., metal-oxide semiconductor field-effect transistor (MOSFET)technologies like complementary metal-oxide semiconductor (CMOS),bipolar technologies like emitter-coupled logic (ECL), polymertechnologies (e.g., silicon-conjugated polymer and metal-conjugatedpolymer-metal structures), mixed analog and digital, etc.

Unless the context clearly requires otherwise, throughout thedescription and the claims, the words “comprise,” “comprising,” and thelike are to be construed in an inclusive sense as opposed to anexclusive or exhaustive sense; that is to say, in a sense of “including,but not limited to.” Words using the singular or plural number alsoinclude the plural or singular number respectively. Additionally, thewords “herein,” “hereunder,” “above,” “below,” and words of similarimport, when used in this application, refer to this application as awhole and not to any particular portions of this application. When theword “or” is used in reference to a list of two or more items, that wordcovers all of the following interpretations of the word: any of theitems in the list, all of the items in the list and any combination ofthe items in the list.

The above description of embodiments of the systems and methods is notintended to be exhaustive or to limit the systems and methods to theprecise forms disclosed. While specific embodiments of, and examplesfor, the systems and methods are described herein for illustrativepurposes, various equivalent modifications are possible within the scopeof the systems and methods, as those skilled in the relevant art willrecognize. The teachings of the systems and methods provided herein canbe applied to other systems and methods, not only for the systems andmethods described above. The elements and acts of the variousembodiments described above can be combined to provide furtherembodiments. These and other changes can be made to the systems andmethods in light of the above detailed description.

In general, in the following claims, the terms used should not beconstrued to limit the systems and methods to the specific embodimentsdisclosed in the specification and the claims, but should be construedto include all systems and methods that operate under the claims.Accordingly, the systems and methods are not limited by the disclosure,but instead the scope is to be determined entirely by the claims. Whilecertain aspects of the systems and methods are presented below incertain claim forms, the inventors contemplate the various aspects ofthe systems and methods in any number of claim forms. Accordingly, theinventors reserve the right to add additional claims after filing theapplication to pursue such additional claim forms for other aspects ofthe systems and methods.

RELATED APPLICATIONS

This application relates to the following related application(s): U.S.Pat. Appl. No. 61/514,369 (filed 2 Aug. 2011), U.S. patent applicationSer. No. 13/565,614 (filed 2 Aug. 2012),U.S. patent application Ser. No.13/565,723 (filed 2 Aug. 2012), U.S. patent application Ser. No.13/565,732 (filed 2 Aug. 2012), each entitled CELL ORGANIZATION ANDTRANSMISSION SCHEMES IN A WIDE AREA POSITIONING SYSTEM (WAPS), and U.S.patent application Ser. No. 15/157,288 (filed 17 May 2016), eachentitled CELL ORGANIZATION AND TRANSMISSION SCHEMES IN A WIDE AREAPOSITIONING SYSTEM (WAPS). The content of each of the relatedapplication(s) is hereby incorporated by reference herein in itsentirety.

The invention claimed is:
 1. A method for broadcasting a plurality ofpositioning signals from a plurality of transmitters in support ofreducing cross-interference in a position location system, the methodcomprising: selecting a first frequency from a sum of a base frequencyplus a first offset that belongs to a set of offsets; generating a firstpositioning signal comprising a carrier at the first frequency, whereinthe first positioning signal includes a first pseudorandom code;transmitting, from a first transmitter, the first positioning signal;selecting a second frequency from a sum of the base frequency plus asecond offset that belongs to the set of offsets; generating a secondpositioning signal comprising a carrier at the second frequency, whereinthe second positioning signal includes a second pseudorandom code;transmitting, from a second transmitter, the second positioning signal,wherein the first positioning signal and the second positioning signalare concurrently transmitted during an interval of time, wherein thefirst offset and the second offset are different by an amount that isequal to or less than 25 percent of the bandwidth of each of theplurality of positioning signals, wherein each of the first and secondpseudorandom codes are repeated for at least N consecutive frames,wherein N is an integer greater than 1, and wherein the first and secondoffsets are chosen such that a circular cross-correlation of the firstand second broadcasted positioning signals over a period of Npseudorandom frames for every lag is either (i) zero in magnitude or(ii) less in magnitude than if the first and second offsets were equal.2. The method of claim 1, wherein the circular cross-correlation of thefirst and second positioning signals over the period of N pseudorandomframes for every lag is zero in magnitude.
 3. The method of claim 1,wherein the circular cross-correlation of the first and secondpositioning signals over the period of N pseudorandom frames for everylag is less in magnitude than if the first and second offsets wereequal.
 4. The method of claim 1, wherein the first and second offsetsare different by an integer multiple of a sum of (i) a frame rate of thefirst and second positioning signals and (ii) a fraction 1/n of theframe rate, where n is an integer.
 5. The method of claim 1, whereineach offset of the set of offsets is a multiple of a minimum nonzerooffset.
 6. The method of claim 5, wherein the set of offsets correspondsto 0,k₀R+R/Q,2k₀R+2R/Q,3k₀R+3R/Q . . . ,(Q−1)k₀R+(Q−1)R/Q, where Rrepresents a PN frame rate, k₀ represents a nonzero integer, and Qrepresents an integer equal to the number of offsets in the set ofoffsets.
 7. The method of claim 6, wherein the integer k₀ has magnitudethat is equal to or greater than two.
 8. The method of claim 6, whereinQ equals a number of PN frames of a positioning signal that is to becoherently integrated by a remote receiver.
 9. The method of claim 1,wherein the first and second offsets are different by an amount that isequal to or less than 10 percent of the bandwidth of each of the firstand second positioning signals.
 10. The method of claim 1, wherein thefirst and second offsets are different by an amount that is equal to orless than 1 percent of the bandwidth of each of the first and secondpositioning signals.
 11. The method of claim 1, wherein the firstpseudorandom code and the second pseudorandom code are differentpseudorandom codes.
 12. The method of claim 1, wherein the firstpseudorandom code and the second pseudorandom code are the samepseudorandom code.
 13. The method of claim 1, wherein the methodcomprises: non-concurrently transmitting two additional positioningsignals during the interval of time using two additional transmitters ofthe plurality of transmitters.
 14. The method of claim 1, wherein themethod comprises: at a receiver, coherently processing an integermultiple of repeated PN frames of one of the first positioning signal orthe second positioning signal.
 15. The method of claim 1, wherein themethod comprises: reducing cross-interference of the second positioningsignal upon the first positioning signal by tuning a receiver to afrequency of the first positioning signal and correlating the firstpositioning signal with a reference pseudorandom ranging signal matchedto a pseudorandom ranging signal of the first positioning signal.
 16. Aposition location system comprising a transmitter network having aplurality of transmitters that broadcast a plurality of positioningsignals in support of reducing cross-interference in the positionlocation system, wherein the plurality of transmitters include a firsttransmitter and a second transmitter, and wherein the position locationsystem includes one or more processors that are coupled to one or morememories and that run one or more applications that perform a method,the method comprising: selecting a first frequency from a sum of a basefrequency plus a first offset that belongs to a set of offsets;generating a first positioning signal comprising a carrier at the firstfrequency, wherein the first positioning signal includes a firstpseudorandom code; transmitting, from a first transmitter, the firstpositioning signal; selecting a second frequency from a sum of the basefrequency plus a second offset that belongs to the set of offsets;generating a second positioning signal comprising a carrier at thesecond frequency, wherein the second positioning signal includes asecond pseudorandom code; transmitting, from a second transmitter, thesecond positioning signal, wherein the first positioning signal and thesecond positioning signal are concurrently transmitted during aninterval of time, wherein the first offset and the second offset aredifferent by an amount that is equal to or less than 25 percent of thebandwidth of each of the plurality of positioning signals, wherein eachof the first and second pseudorandom codes are repeated for at least Nconsecutive frames, wherein N is an integer greater than 1, and whereinthe first and second offsets are chosen such that a circularcross-correlation of the first and second broadcasted positioningsignals over a period of N pseudorandom frames for every lag is either(i) zero in magnitude or (ii) less in magnitude than if the first andsecond offsets were equal.
 17. The position location system of claim 16,wherein the circular cross-correlation of the first and secondpositioning signals over the period of N pseudorandom frames for everylag is zero in magnitude.
 18. The position location system of claim 16,wherein the circular cross-correlation of the first and secondpositioning signals over the period of N pseudorandom frames for everylag is less in magnitude than if the first and second offsets wereequal.
 19. The position location system of claim 16, wherein the firstand second offsets are different by an integer multiple of a sum of (i)a frame rate of the first and second positioning signals and (ii) afraction 1/n of the frame rate, where n is an integer.
 20. The positionlocation system of claim 16, wherein each offset of the set of offsetsis a multiple of a minimum nonzero offset.
 21. The position locationsystem of claim 20, wherein the set of offsets corresponds to 0,k₀R+R/Q, 2k₀R+2R/Q, 3k₀R+3R/Q . . . , (Q−1)k₀R+(Q−1)R/Q, where Rrepresents a PN frame rate, k₀ represents a nonzero integer, and Qrepresents an integer equal to the number of offsets in the set ofoffsets.
 22. The position location system of claim 21, wherein theinteger k₀ has magnitude that is equal to or greater than two.
 23. Theposition location system of claim 21, wherein Q equals a number of PNframes of a positioning signal that is to be coherently integrated by aremote receiver.
 24. The position location system of claim 16, whereinthe first and second offsets are different by an amount that is equal toor less than 10 percent of the bandwidth of each of the first and secondpositioning signals.
 25. The position location system of claim 16,wherein the first and second offsets are different by an amount that isequal to or less than 1 percent of the bandwidth of each of the firstand second positioning signals.
 26. The position location system ofclaim 16, wherein the first pseudorandom code and the secondpseudorandom code are different pseudorandom codes.
 27. The positionlocation system of claim 16, wherein the first pseudorandom code and thesecond pseudorandom code are the same pseudorandom code.
 28. Theposition location system of claim 16, wherein the method comprises:non-concurrently transmitting two additional positioning signals duringthe interval of time using two additional transmitters of the pluralityof transmitters.
 29. The position location system of claim 16, whereinthe method comprises: at a receiver, coherently processing an integermultiple of repeated PN frames of one of the first positioning signal orthe second positioning signal.
 30. The position location system of claim16, wherein the method comprises: reducing cross-interference of thesecond positioning signal upon the first positioning signal by tuning areceiver to a frequency of the first positioning signal and correlatingthe first positioning signal with a reference pseudorandom rangingsignal matched to a pseudorandom ranging signal of the first positioningsignal.
 31. A position location system for broadcasting a plurality ofpositioning signals from a plurality of transmitters in support ofreducing cross-interference in a position location system, the systemcomprising: means for selecting a first frequency from a sum of a basefrequency plus a first offset that belongs to a set of offsets; meansfor generating a first positioning signal comprising a carrier at thefirst frequency, wherein the first positioning signal includes a firstpseudorandom code; means for transmitting, from a first transmitter, thefirst positioning signal; means for selecting a second frequency from asum of the base frequency plus a second offset that belongs to the setof offsets; means for generating a second positioning signal comprisinga carrier at the second frequency, wherein the second positioning signalincludes a second pseudorandom code; means for transmitting, from asecond transmitter, the second positioning signal, wherein the firstpositioning signal and the second positioning signal are concurrentlytransmitted during an interval of time, wherein the first offset and thesecond offset are different by an amount that is equal to or less than25 percent of the bandwidth of each of the plurality of positioningsignals, wherein each of the first and second pseudorandom codes arerepeated for at least N consecutive frames, wherein N is an integergreater than 1, and wherein the first and second offsets are chosen suchthat a circular cross-correlation of the first and second broadcastedpositioning signals over a period of N pseudorandom frames for every lagis either (i) zero in magnitude or (ii) less in magnitude than if thefirst and second offsets were equal.
 32. The position location system ofclaim 31, wherein the circular cross-correlation of the first and secondpositioning signals over the period of N pseudorandom frames for everylag is zero in magnitude.
 33. The position location system of claim 31,wherein the circular cross-correlation of the first and secondpositioning signals over the period of N pseudorandom frames for everylag is less in magnitude than if the first and second offsets wereequal.
 34. The position location system of claim 31, wherein the firstand second offsets are different by an integer multiple of a sum of (i)a frame rate of the first and second positioning signals and (ii) afraction 1/n of the frame rate, where n is an integer.
 35. The positionlocation system of claim 31, wherein each offset of the set of offsetsis a multiple of a minimum nonzero offset.
 36. The position locationsystem of claim 31, wherein the set of offsets corresponds to 0,k₀R+R/Q, 2k₀R+2R/Q, 3k₀R+3R/Q . . . , (Q−1)k₀R+(Q−1)R/Q, where Rrepresents a PN frame rate, k₀ represents a nonzero integer, and Qrepresents an integer equal to the number of offsets in the set ofoffsets.
 37. The position location system of claim 36, wherein theinteger k₀ has magnitude that is equal to or greater than two.
 38. Theposition location system of claim 36, wherein Q equals a number of PNframes of a positioning signal that is to be coherently integrated by aremote receiver.
 39. The position location system of claim 31, whereinthe first and second offsets are different by an amount that is equal toor less than 10 percent of the bandwidth of each of the first and secondpositioning signals.
 40. The position location system of claim 31,wherein the first and second offsets are different by an amount that isequal to or less than 1 percent of the bandwidth of each of the firstand second positioning signals.
 41. The position location system ofclaim 31, wherein the first pseudorandom code and the secondpseudorandom code are different pseudorandom codes.
 42. The positionlocation system of claim 31, wherein the first pseudorandom code and thesecond pseudorandom code are the same pseudorandom code.
 43. Theposition location system of claim 31, wherein the system comprises:means for non-concurrently transmitting two additional positioningsignals during the interval of time using two additional transmitters ofthe plurality of transmitters.
 44. The position location system of claim31, wherein the system comprises: at a receiver, means for coherentlyprocessing an integer multiple of repeated PN frames of one of the firstpositioning signal or the second positioning signal.
 45. The positionlocation system of claim 31, wherein the system comprises: means forreducing cross-interference of the second positioning signal upon thefirst positioning signal by tuning a receiver to a frequency of thefirst positioning signal and correlating the first positioning signalwith a reference pseudorandom ranging signal matched to a pseudorandomranging signal of the first positioning signal.
 46. A position locationsystem for broadcasting positioning signals in support of reducingcross-interference, the position location system comprising: a pluralityof transmitters that are configured to transmit a plurality ofpositioning signals, wherein the plurality of transmitters include: afirst transmitter that is configured to generate and transmit a firstpositioning signal comprising a carrier at a first frequency selectedfrom a sum of a base frequency plus a first offset that belongs to a setof offsets, wherein the first positioning signal includes a firstpseudorandom code; a second transmitter that is configured to generateand transmit a second positioning signal comprising a carrier at asecond frequency selected from a sum of the base frequency plus a secondoffset that belongs to the set of offsets, wherein the secondpositioning signal includes a second pseudorandom code, wherein thefirst positioning signal and the second positioning signal areconcurrently transmitted during an interval of time, wherein the firstoffset and the second offset are different by an amount that is equal toor less than 25 percent of the bandwidth of each of the plurality ofpositioning signals, wherein each of the first and second pseudorandomcodes are repeated for at least N consecutive frames, wherein N is aninteger greater than 1, and wherein the first and second offsets arechosen such that a circular cross-correlation of the first and secondbroadcasted positioning signals over a period of N pseudorandom framesfor every lag is either (i) zero in magnitude or (ii) less in magnitudethan if the first and second offsets were equal.
 47. The positionlocation system of claim 46, wherein the position location systemcomprises a receiver that is configured to reduce cross-interference ofthe second positioning signal upon the first positioning signal bytuning a receiver to a frequency of the first positioning signal andcorrelating the first positioning signal with a reference pseudorandomranging signal matched to a pseudorandom ranging signal of the firstpositioning signal.
 48. The position location system of claim 46,wherein the circular cross-correlation of the first and secondpositioning signals over the period of N pseudorandom frames for everylag is zero in magnitude.
 49. The position location system of claim 46,wherein the circular cross-correlation of the first and secondpositioning signals over the period of N pseudorandom frames for everylag is less in magnitude than if the first and second offsets wereequal.
 50. The position location system of claim 46, wherein the firstand second offsets are different by an integer multiple of a sum of (i)a frame rate of the first and second positioning signals and (ii) afraction 1/n of the frame rate, where n is an integer.
 51. The positionlocation system of claim 46, wherein each offset of the set of offsetsis a multiple of a minimum nonzero offset.
 52. The position locationsystem of claim 51, wherein the set of offsets corresponds to 0,k₀R+R/Q, 2k₀R+2R/Q, 3k₀R+3R/Q . . . , (Q−1)k₀R+(Q−1)R/Q, where Rrepresents a PN frame rate, k₀ represents a nonzero integer, and Qrepresents an integer equal to the number of offsets in the set ofoffsets.
 53. The position location system of claim 52, wherein theinteger k₀ has magnitude that is equal to or greater than two.
 54. Theposition location system of claim 52, wherein Q equals a number of PNframes of a positioning signal that is to be coherently integrated by aremote receiver.
 55. The position location system of claim 46, whereinthe first and second offsets are different by an amount that is equal toor less than 10 percent of the bandwidth of each of the first and secondpositioning signals.
 56. The position location system of claim 46,wherein the first and second offsets are different by an amount that isequal to or less than 1 percent of the bandwidth of each of the firstand second positioning signals.
 57. The position location system ofclaim 46, wherein the first pseudorandom code and the secondpseudorandom code are different pseudorandom codes.
 58. The positionlocation system of claim 46, wherein the first pseudorandom code and thesecond pseudorandom code are the same pseudorandom code.
 59. Theposition location system of claim 46, wherein the system comprises: twoadditional transmitters of the plurality of transmitters that areconfigured to non-concurrently transmit two additional positioningsignals during the interval of time.
 60. The position location system ofclaim 46, wherein the system comprises: a receiver that is configured tocoherently process an integer multiple of repeated PN frames of one ofthe first positioning signal or the second positioning signal.